I am the academic director of future learning and we started with this idea of having a technology enhanced language school and that brings the question, what is technology enhanced learning and what is it not? Because people have ideas about that when you mention that that's what you're trying to do that needs a little bit of clarification and explanation. So this short talk is about that. A little bit of background, we are focusing on junior courses, international learners. We started in 2013 with this idea of bringing technology into the language teaching classroom and we started with 45 students and we had 4,000 students in the last year and some schools in four locations and now we started to do these short stay programs for the common school tours and to do projects, technology based projects as well, high school, integrations and we're thinking about how do we bring it into other programs as a new departure and we got funding from the local enterprise board and we were very proud to be accredited by EQUALS recently. And so these are what my students kind of look like, like that, and we get them from France and Spain and Poland and China and we do technology enhanced language projects with them and so let's start with this, what's learning technology for you? Now have here the essential piece of kit for many teachers. So who uses one of these? So you already are dependent on technology in your classes. You're using this, you're dependent on technology in your classes and you've had those moments when it breaks down, yeah, anybody have something to pull a copy of break down recently? Yeah, okay, you're like, oh my God, it's broken down. And so I always mention that because people are kind of like, I can't use technology because you can't depend on it, but if it breaks down and I'm trying to say, well you're already depending on some key piece of technology that sometimes break down and you live with it. And so to extend technology into other areas is not that big a leap from, you know, the forward copier has broken down, the Wi-Fi has broken down, you find a way around it, you have a class that works to keep you going until it gets repaired or whatever. It's the same problem that they're already dealing with. It's not a new problem. And people are like, oh, this is a whole new problem. No, it's the same problem. It's just it would just like a new varnish or a new, a new presentation. And so opening out this idea of what is learning technology, I want to throw in some other suggestions. Anybody recognize what that is? Feltboard. And I put that up there because when I was in primary school, the Irish classes were done with the feltboard where the teacher would tell a story using the little characters and teaching us the language. And so there's a bit of felt crow on it and they stick them on and move them around and so on. An obvious one. Of course you can't forget about that, a technology in its way, you know, people were able to do things with it that they weren't able to do before in terms of conveying information to the students or helping them understand things. And I put this one up here because, you know, it's not just a piece of art. It's about trying to help people understand a story, a complex story. It's a teaching tool. It's a visual teaching tool. There is that element as well. Of course now we have these or there's one there, yeah. Anybody use one of those? Yeah, notoriously for getting stuck on the carousel as the slides go round. Yeah. What about one of these? It's a hand crank printer. Yeah. It's also called a Gestetner machine. So it's a precursor of the copier. You have to cut the stencil, put it in, you can squeeze through and you turn the handle and the pages come out. And what were one of these? Yeah, one of these. And the thing I thought I was missing, of course, was for the language teaching classroom. Yeah. One of those with the counter. So you could make sure that you're reliant to the correct spot. And so all of that is by way of saying learning technology is any device which assists learning. It doesn't need to be electronic. But any device which assists learning is a learning technology. It changes what we do and how we do it. So I'm going to give you a moment just to talk to the person beside you about which of these learning technologies you have used or have been used on you and are there any others that you think that you think I've missed? Okay, so one minute. Can you please talk for a minute? No, no, no, I'm looking for you. Thank you very much. I think we might have used a lot of the projectors. You have those kind of transparency right on the top of down the loose. That's a nice handwriting. Okay, I'm going to stop that there. I'm going to run it in time. Did I miss any? Did anybody want to throw in another learning technology? A TV set. A TV set, yes, with the VHS report. What was that? The smart board. The smart board, yes. There it is right there in the flesh. So that's where we are. We're using this technology. But then it's a question of enhanced learning and what does that mean? Because the problem with technology is that it seems to be a good in itself that as soon as you have technology, the students are going to learn. But there's a problem there. Technology doesn't teach the students. And so it's just a tool and you have to think about what are you going to do with that tool to make it effective. So when I'm trying to explain that we're using technology in our language learning classrooms, then this is the idea that I've adopted about technology. So I'm opening out the definitions as much as possible. The learning is any use of information and communication technology, any use. Even if it's your audio recordings or anything, that is using the digital learning, using the electronic learning. We're already doing it. It's not the future. It's now. And my definition of enhanced is we use that technology when big bold capital letters, it can help improve the learning outcomes. And by that I mean through engagement of the students, making them more interested, a better way to convey the information, helping them practice more, motivating them and then individualizing in a way that the teacher talking to the whole room just can't. Whoever is using it. So it doesn't need to be in the hands of the learners straight away. It could be in the hands of the teachers like me here to you. It could be in the hands of the managers or the administrators, tracking students progress and seeing how they're doing and all of that. And of course in the hands of the learners is also important as well, but it's not the only enhancement. And so I'm opening that out to show how much we're already here in this, in the middle of this unquestioningly enhancing, doing technology enhanced learning. And so I want to make that conscious. People ask when I say technology enhanced language learning, they ask, well is it a technology course? And the answer is no. Students might learn how to use a language learning application more effectively, but that's not the primary goal. It's still a language course. And then they go, well is it online? And I don't think it has to be online to be technology enhanced. It can supplement face-to-face teaching. It can enhance our face-to-face teaching.  They're using their dictionary apps as part of their face-to-face learning. We already live in that world. And so I'm insisting on the need to teach communication face-to-face. I don't see that technology takes that away, but it is increasingly going to be part of it. I'm sorry, I put the future tense in there. It is increasingly part of it in the now, in the present. And so what do you need? You need an inspirational quote to conclude your presentation. And this is the one that explains why. Why we have to use technology in classroom. Because, of course, there are a lot of reasons that it brings problems with it. You have the attention span problem and how do you keep people focused and all of those difficulties and what information is true and what do you believe and all of that. And so you have to deal with those things if you're going to bring technology into the classroom. But it's not a valid choice to say we don't deal with them because it's the pen and paper of our time. It's the lens through which we or our students experience the world. And so teaching them to manage those problems that come with it is part of our job as educators. It's essential for them to function in the world. Because we could keep them in the classroom bubble wrapped up and bubble wrapped and say, you know, there won't be any distractions or there won't be any false information. It can all be safe and reliable and soothing and calming. And then put them out into the real world and they can't cope with that. It's like the classic thing where the teacher or the student says to me, teacher, I understand you. I don't understand anyone else. And so it's a bit like that that we can make it too safe. This one is to do with don't forget the teachers. And our government is bringing in a secondary school technology policy that's all about hardware. That's all about infrastructure. And it's not put the money into training the teachers and then you don't necessarily need a smart board to make the technology work in the classroom and to spend all the money on the infrastructure. But if you do spend all the money on the infrastructure and none on the teachers, then it's wasted, completely wasted, right? So if the teachers are not able, then it will fail. Technology will not do the teaching. The teachers will. It's just a tool. Cannot substitute for well-trained teachers, says this guy from the consortium of school networking in the United States. It's like a textbook won't teach students. I suppose we have to be honest and say there are a minority of self-teaching students that don't need teachers. But there are very small minority of people who can actually teach themselves. But for the majority of students, the book is not going to teach them without help from the teacher. The software is not going to teach them without help from the teacher. People need the structure. They need the direction. They need the encouragement, the motivation, the feedback, all of that stuff that can only come from the teacher. But if you're going to bring it in, you can't have it as a special event. You can't have, well, once a month there's going to be a technology day when we have a technology team in our technology classroom. That won't do it. It has to be integrated. It has to be the students get used to it. They learn how to do it. They learn how to use it effectively. It becomes another tool that they have learned, like a dictionary. You can't just have a dictionary day and use it once in a while. It has to be a regular part of...


We didn't really give the Obama administration enough time. Eight years wasn't enough. There was something beginning to happen that started Underholder and then Lynch at the Justice Department where they began to prosecute corporations. They put the private colleges. They didn't necessarily put them out of business, but they put a lot of private universities out of business. They're kind of putting private prisons out of business. And I was getting really optimistic that if Hillary became president, this would continue. And we'd see something that we really have not seen for decades. I don't even think we saw it under the Clinton administration where the Justice Department began to say, OK, if corporations are people, then the people in those corporations are, well, not going to go to prison, but they're going to be fine. We're going to go after them. We were beginning to see that recently, weren't we? Yeah, absolutely. And we're not going to see that now. This is a new... He's basically putting people in charge of cabinet positions that they want eliminated. For example, Rick Perry, the former governor of Texas, the longest serving governor of Texas. He's been nominated to run the Department of Energy. That's the department he couldn't remember. He had three departments he wanted to eliminate during his 2012 debate, oops, moment. So it's always good for Exxon when a mouth breather is running energy. This is especially good for Exxon if this specific intellectual lightweight, Rick Perry, is running energy. Yes, running energy and our nuclear weapons as well. A lot of nuclear energy is what they work on a lot there. So as kind of we've talked about a lot, all of these nominees and these kind of critical cabinet positions have been funded in their political roles by ExxonMobil. And Rick Perry is no different. He has taken $40,000 just in his most recent gubernatorial election from ExxonMobil. And in his role at the Department of Energy, if he's confirmed, he would be overseeing a lot of research into ExxonMobil's competitors in alternative fuels and electric vehicles. And so that kind of stuff could really go away without funding being directed towards it. You're listening to highlights from The David Feldman Show, heard nationwide on Pacifica Radio, or as a podcast on iTunes, Stitcher, and now YouTube. Please subscribe to this channel. For more information, go to davidfeldmanshow.com. Thank you for listening. Oops.


Hello, in this video we will focus on impedance matching and filtering of the RF part of the STN32WL. The RF circuits between the STN32WL and the antenna can be divided into three main parts, transmitter impedance matching and filtering, receiver impedance matching and balloon, and the antenna matching network. There is a lot of information on this topic which has been divided into several shorter videos. This video covers the analytical description. It shows meaning and basic principle of each block. To illustrate the principle, calculations are based on idle components and conditions. Then there is another series of videos showing practical measurement taken on a real board, in this case STN32WL nuclear board. The series contains several videos, each focusing on a different part of RF circuit. Why is this topic about impedance matching and filtering needed? Impedance matching is needed for optimization of working conditions for the selected band. For minimizing power loss due to impedance mismatch, for example in case of transmitter it improves output power and in case of receiver it improves sensitivity. And to optimize overall energy consumption. In case of filtering, the transmitter is based on a highly efficient, non-linear class of RF power amplifier that generates significant harmonic spectral content at the expense of power consumption. These products must be filtered to pass regulatory certification limits. In this slide, we will focus on the transmitter part. The antenna cannot be connected directly to the transmitter output of the STN32WL due to impedance mismatch and spectral content of the signal. The radiated power would be low and can violate regulatory limits due to unwanted spectral content. If we add matching network, it helps with impedance mismatch. The radiated power will be maximized. The spurious and harmonic products remain. To suppress these products, a filter must be added to the signal path. Now the signal has parameters we wanted and can be transmitted by the antenna. STN32WL has two transmitter outputs, one low power and one high power. If both outputs are used in the design, each needs its own impedance matching and filter. In case of receiver part, we cannot also connect the antenna directly. The receiver input is differential and has different impedance than the antenna. We need to implement Balloon, which transforms single-ended signal to differential under impedance matching network. It minimizes impedance mismatch and improves receiver sensitivity. Typical RF circuit, which implements both transmitter and receiver parts, looks like this. We can see the blocks we discussed earlier for isolated transmitter and receiver. What is new is the RF switch which switches the antenna to the transmitter or receiver part. The system is half-tuplex. It means it can transmit or receive but not at the same time. This structure is general, but there are also some variants. One uses IPD, which means Integrated Passive Device. The IPD is a component that implements all passive components like Balloon, matching network and filters in one component. It's smaller and easier to implement that variant with discrete parts. Another variant doesn't use RF switch. Both transmitter and receiver parts are connected in one point. This is cheaper and easy to implement. This advantage is a worse transmitter and receiver performance. The RF switch normally serves also as an isolator, which isolates both parts. Now this isolation is missing. In this video, we will discuss variant with the RF switch. Okay, let's take a closer look at the transmitter path. As we mentioned earlier, spectral content of the transmitter output can be very rich. With the desired signal, there are harmonic frequencies and discrete spurs. These unwanted products must be suppressed. The signal that we want at the antenna may look like this. The desired signal is maximized. This can be achieved by good impedance matching. All harmonics and spurious products are below regulatory limits. The transmitter path can be divided into several smaller parts. Power amplifier biasing and filtering. Transmitter matching network, notch filter, low pass filter, RF switch and the antenna matching network. These C blocks are needed for the RF switch operation. The RF switch and the antenna matching network are shared with the receiver path. Here is a principle scheme of the transmitter output. Internal power regulator powers the power amplifier transistor through the RF choke. Output signal is not harmonic, spectral content is rich. To get the right signal, it must be filtered and matched. STM32WL has two output pins, which differ in output power. Low power output, which has output power up to 15 dBm and high power output, which has output power up to 22 dBm. Impedance of the output pins is not 50 ohm. It is also not a constant value. The impedance depends on many parameters like package, frequency, transmitted output power and also PCB layout. We measured optimal loading or matching impedances of the output pins to simplify design of the matching network. Detailed measurements can be found in the application node AN 5457. Here is the recommended structure of the power amplifier biasing. A voltage from the internal regulator powers the power amplifier through the RF choke. Impedent value depends on the working band, the two capacitors, filter, the voltage. Their value is fixed. The purpose of this block is to match the power amplifier output impedance to 50 ohms. For example, for frequency 868 MHz at 14 dBm, the optimal loading impedance is this value. We can assume power amplifier impedance as complex conjugated value of the optimal loading impedance. Based on this, equivalent circuit of the power amplifier output can be modeled as a series connection of a resistor and a capacitor with these values. In the block diagram, we can see equivalent circuit of the power amplifier output, power amplifier bias circuit and the matching network structure which match the power amplifier impedance to 50 ohms. Values of the matching network components can be calculated in the Smith chart. If this point is impedance of the power amplifier, then if we use these values of a serial inductor and parallel capacitor, we get 50 ohms at the output. If the distance between the RF output pin and the matching network is too long, we must consider also impact of the transmission line. It means that impedance at the beginning of the transmission line is transformed to another impedance at the end. This depends on the length and impedance of the transmission line. Another block is the notch filter which suppresses the second harmonic. Here is the filter structure. Recommended values can be obtained by the following steps. L2 is about three quarters of L1. Resonance frequency of L2 and C2 is around second harmonic frequency. To have a good matching, C1 and C3 might be tweaked. In this chart are ideal return loss and transmission of the notch filter. It's matched for the fundamental harmonic and suppresses the second harmonic. Matching of the filter can be calculated in the Smith chart. The low pass filter filters the higher harmonics. Recommended structure is P-ledder network. Second filter approximation is third order Chebyshev which is matched for the fundamental frequency. Here is an example of the filter and the simulation results. We can see impedance matching and transmission. Black curves are results with ideal components and the red ones are results with S-parameters of real components. Power capacitors of the filter can be affected by adjacent capacitors. In this case, these capacitors must be adjusted. Capacitors between the notch filter and the low pass filter can be combined into one capacitor. The capacitor close to the RF switch is usually lower due to parasitic capacitance of the RF switch. The RF switch switches shared antenna to the transmitter or receiver circuit. It also isolates transmitter and receiver branches. Typical parameters of the RF switch are listed here. For example, the following RF switches can be used in designs with STM32WL. The DC blocks block DC current to the RF switch. They are mandatory for some RF switches. DC block capacitors might have little effect on the parameters of the low pass filter. When fine tuning the low pass filter, the effect of these DC blocking capacitors must be taken into account. Now let's take a closer look at the receiver path. Calls of the receiver circuit are impedance matching to have good receiver sensitivity and single ended to differential signal conversion. Typical structure of the receiver circuit looks like this. A brief, simplified description of the components is as follows. Inductor L5 matches reactive path of the LNA. This inductor is used for impedance matching together with C11, C12 is a path of so-called balloon light circuit, and C13 can be used for impedance matching or reducing of harmonics. This analytical structure can be simplified like this. This structure is implemented in reference designs with STM32WL. Like the transmitter, also receiver impedance is not 50 ohms or a fixed value. This depends on many parameters like package, frequency or PCB. Recommended matching on the impedances were measured and are described in application note 5457. On the right side is the example of the matching in the Smith chart. We assume QFN package and frequency 868 MHz. Compatible impedance for these parameters is 52 plus J102 ohms. We start matching from the receiver side, so we use complex conjugated value. The goal is to set L5 and capacitors C11 and C12 to get as close as possible to 50 ohms in the Smith chart. Differential transmission line between the STM32WL receiver pins and the nearest passive components has also impact to the optimum values of these passive components. The greater the length, the more it transforms the impedance. This must be taken into account when fine-tuning the receiver matching network. Balloon converts single-ended signal to differential. In designs with STM32WL we don't implement real balloon but so-called balloon-like circuit. It consists of three components. Detailed calculation of these components can be found in the application note 5457. This structure has less losses than the real balloon. The main difference between the balloon and this balloon-like circuit is that this circuit has no exact 180° phase difference. An exact 180° phase difference would only exist if the equivalent input resistance of the LNA was very large. This balloon-like circuit is a good compromise between cost, PCB surface, losses, and performance. Now let's discuss the antenna matching network. The antenna matching network matches the antenna impedance to 50 ohms. Typically, it has p-ladder topology on the PCB but only one half is usually used. The values of the components depend on the specific impedance of the antenna. For example, if the antenna has impedance 20 plus J10 ohms, we can use an inductor L4 and capacitor C7 with these values to get to 50 ohms. C8 is unused. If the antenna matching network is in the right configuration, for example CLC structure, it also behaves like a low-pass filter. This additional filter is needed if the high-power output is used. It's because high-power output generates strong harmonics and in regions where this power is allowed are more strict requirements for harmonics level. The matching and filtering properties of the CLC structure must be fine-tuned together. If the high-power output is used and the antenna matching needs a different structure than a low-pass filter, then additional Pi section for low-pass filter is recommended. It can be used also if better margin from the certification level is needed for harmonics and spurious. Adjacent components can be used as one component if they are of the same type. Few words at the end. For easier explanation, calculations in this video use ideal components, but in the real world additional effects must be considered, for example, behavior of real components, impact of the PCB layout, tolerance of components, temperature, etc. In this picture we can see simulated forward transmission of the low-pass filter. We can see results based on ideal components, real components and the real components with impact of the PCB layout. More accurate results can be obtained by electromagnetic field simulation or measurement on a prototype. More information about this topic can be found in the following application notes. Reference designs can be also useful source of information. Thank you for your attention.


Okay, we're back, this is Dave Vellante, and I'm with Stu Miniman, we're with Wikibon.org, and this is SiliconANGLE.tv's The Cube, and we're here at the Dell Storage Forum in Boston 2012, and we're here with Carter George. Carter is the executive director of Dell's storage strategy and came to Dell via an acquisition. We're talking at the top of the show about Dell's very aggressive acquisitions. He came from Ocarino, which is a storage optimization specialist. Carter, welcome to The Cube. Thanks, it's good to be here. I believe this is your first time on The Cube. It is, yeah. Hopefully, we will see you many more times. So, executive director of the Dell Storage Strategies, you've got a growing portfolio that you're looking after, so tell me in a nutshell, what is Dell's storage strategy? Well, we're a company in transition. Dell is becoming more and more of a solutions provider rather than just a seller of products and storage is really a key part of that. In storage, that transition really is manifesting itself as a shift from being a reseller of other people's products to being a true storage company where we create new IP, new solutions, and actually soup to nuts to develop new storage stuff and bring it to market. And the sort of core vision that we have there that frames all of those acquisitions and the other things that we're doing, it's sort of a virtuous circle where the first half is bringing high-end enterprise feature function down to the mid-market customer, being able to do things that may be previously only the Fortune 500 data center could have afforded to do. We want to bring those to a much broader audience. And as we succeed in doing that, then we should also have created mid-range products that we could take and change the economics of enterprise storage with. So, what's an example of some of those functions that you'd expect, you know, Fortune 50, a Fortune 500 company to have that SMB traditionally have not been able to access? Well, for example, all of our storage architectures are scale out where we take industry standard building blocks and allow you to group those together to make small, medium, large, extra-large systems. So, a small customer might buy just one at a very, you know, reasonable price point. A large customer might buy seven or eight or ten of those and group them together and be able to do a high-end thing for a fraction of the cost that a traditional high-end enterprise thing might have cost. Can you talk a little bit about integration? So, you've got all these assets that you've acquired. And oftentimes, storage companies will acquire these assets and just let them be.  My sense is Dell has a different strategy there. Is that true? And can you talk about the integration? Very much so. Our ambitions are much more aggressive. We're really trying to take one plus one and get three out of it. So, when we look at these acquisitions, they're all building blocks towards building, towards this fluid data vision of the future that we have. I mean, we really looked out three to five years and said, what kind of problems are customers going to be facing in storage?  And we said, what does storage need to look like then? And we've set out to get the pieces we need to put that together. And, you know, you're going to see really starting this year and on into the future, a Dell storage personality emerging where, you know, the things that we've acquired will start to look more consistent and compatible and more like a Dell thing rather than the thing, the standalone thing that we bought. So, you talk about fluid data architecture and fluid data vision. Tell us why, tell us what that is, you know, it sounds like great marketing, but tell us why it's more than just great marketing. What's underneath the covers? Well, fluid data is our architectural vision of how storage needs to work together to solve customer problems. There's several tenets to it, like that scale out design is one of those. Right place, right time is another one where we feel data needs to be able to move from one place to another to get data to the right place at the right time. Transparently without having expensive storage admins or a lot of manual process, we really feel like the building blocks need to work together by policy and automatically to do the things that need to get done. And that's what fluid data is really all about. You know, we like that sort of fluid metaphor, water seeks its own level, you know, it flows to the right place. And it was a phrase that Compellent had used. And before we acquired Compellent, we really still liked that fluid idea. But you know, we looked at alternatives, wet data, no, liquid data. It wasn't really working for us. So when we got Compellent, we really liked the phrase. And now we've extended it to talk about the whole, the whole picture. So when you think about fluid day, one more, if I may say, when you think about fluidity, and because we I met you when you first were at Ocarina, and you think about moving data around the storage portfolio. And a lot of times you've got to, you know, optimize the data, whether you compress it or de-dupe it, and then you got to rehydrate it. And that, you know, that's that's time intensive, it's overhead intensive. Is that part of the vision where you can actually seamlessly move data throughout the storage portfolio without having to rehydrate? And is that part of the actual execution? Yeah, absolutely. I think, you know, two key concepts are tearing data to get it to the right place. And that means both, you know, traditional tearing up and down inside a product set, you know, that sort of thing, but also horizontal tearing where we move data from one product to another through a workflow. And if you think about that, optimization becomes really important. If you're going to programmatically be moving data from one platform to another on a regular basis, you really need to make that very efficient. And so, you know, de-dupe compression, erasure coding, thin provisioning, these are all ways to get the data smaller and keep it small while you're moving it. And, you know, when I talk about a Dell personality emerging, you'll start to see some things be consistent and compatible across multiple products. And de-dupe is one of those and compression. The Ocarina technology is being integrated into the file system, into the object store, into the backup target, into the components, into the equal logic, and eventually you'll have that consistent and compatible de-duping compression on every Dell platform. And that means that we can move data in its most de-duped and compressed form without having to rehydrate it. Just to, we've been talking a lot on the cube about converged infrastructure for the last several, you know, months, you know, a couple years now. Take it away. Absolutely. So actually, Dave, I was wondering if I could take a slightly different direction. We talked about kind of your Ocarina, the de-duping compression. Most people really know, you know, the equal logic exanet on the NAS side and compelling. The more recent acquisitions of RNA networks and APA-sure, can you kind of frame up where those fit in the portfolio and just give us a little bit of data as to what those are? Yeah, absolutely. So RNA, a very small company, one that probably not a lot of people have heard of, but it's become a very important part of our plans going forward. You know, we talked about tiering and Dave mentioned converged infrastructure. RNA is a software platform that lets us extend our storage up into the application server. So if I think of a platform like Compellent, you know, it supports a very rich set of tiers inside the Compellent. What we want to be able to do is extend that tiering up into the application server so that resources like Flash or SSD that are in the application server can become logically part of the storage. We can move hot data right next to the CPU and access it there while still having things like snapshots and replication and so forth that are driven in the storage be consistent and accurate. So we're really excited about RNA and you'll be hearing more about that through the course of this week. Apisher is our first foray into the world of data protection. And, you know, that's a very important topic for most customers. And we, as part of fluid data, are forecasting a major convergence of what historically have been two separate and independent areas of data protection backup software and the whole area of snapshots and replication. We see these two things coming together into a single managed data protection environment. And Apisher is the platform that we're going to build build that around. Okay, great. So if we look specifically at converged infrastructure, so obviously, Dell's got the components, you've got server, you've got networks. And you've got, you know, the storage pieces.  So can you talk about how all these these different software pieces and these acquisitions kind of roll into like the VIS orchestrator that you guys have for your convergence? Yeah, we do have orchestration and automation happening at the server layer with VIS. And we also have what we call workload aware storage management being developed in Dell Storage. And that will provide a framework that we can plug into VIS, but also other server management things like vCenter, for example, or the Microsoft Management Suite. So we'll have a consistent way that you can reach out and manage Dell storage, whatever the orchestration layer is that customer chooses. And that will include a Dell Storage API, let's call it, that if a developer or manager writes to that API, in turn, that will manage all the different Dell storage elements. So you don't have to develop specifically for equal logic or for compelling or for our file system, for things like provisioning, and so forth. You can write to one API, and that'll take care of it for the whole portfolio. Great, that kind of builds if you saw IBM's recent announcement on Pure Systems, they called it kind of the expert aware, it's understanding that workload, and how it fits in the entire solution. So it sounds like what you're talking about kind of the workload aware is kind of along that same vein. Absolutely.  Sure, I might need 10 terabytes of space. But I'm also trying to figure out is that a fast 10 terabytes or slow 10 terabytes? Is it a highly protected, fault tolerant 10 terabytes or just a pool of you know, storage that I can throw stuff in. And what we'd like to see is the storage infrastructure taking care of that for you. If you say I need 10 terabytes for VMware or for exchange or for a mission critical database, there'll be some templates there that will help you solve for the protection level, the performance level and the capacity. Carter, the flash market's pretty frothy right now. You just saw, you know, one of your competitors made a big acquisition, you know, reportedly at 400 million in change for a company that doesn't even have product out, you're seeing valuations, you know, huge for, again, companies that don't have product or in the case of say violin memory and $800 million valuation, you know, reported you see fusion IO. What's your take on the whole flash situation? Is it as game changing as a lot of people believe in what's what's Dell's angle? Yeah, we really believe it is. I think we expect in most customers within three years, let's say most active data will have moved from disk to memory. Now that doesn't mean all your data, the average customer has 10 15 20% of their data is active and the rest of it is some version of cold. So we're talking about the active data, but we really see a major paradigm shift as that active data moves to memory based storage. And, and, you know, we expect Dell to be a leader in that space. This is an area where converged infrastructure really does matter because as servers get faster and faster and faster, storage has to get faster to keep up with the capability of those cores. And the best place to be if you want to be fast is close to the CPU. So with things like RNA, we're going to be enabling memory based storage, not only in the shared storage fabric on compelling and equal logic, but also right up there on the same bus as the CPU. And our goal is to tie that all together into a single coherent fabric. So it's just it feels like there's a and by the way, we would agree, we think most if not all active data will be on flash within the next three to five years. And it seems like from an application development standpoint, there's a real opportunity to change the way in which we've written applications for the last 40 years, you know, sort of reach around reaching around the horrible storage stack, if you will, talk about developers. You mentioned, you know, the Dell Storage API. What is Dell's sort of reach out to developers? There's a big movement around DevOps, you know, the intersection of application development and operations, infrastructure operations. What are your thoughts on that, particularly as how it relates to new applications that might come into the marketplace? Well, I guess we sort of view that as two different audiences for the application developer, the, you know, the group building business applications in support of a company's mission. We're not really asking them to do anything different or unique to Dell. We want to deliver storage that's compatible with the ways that they do things today, with the tools that they use and so forth and to allow this cool new infrastructure to just fit in there transparently. For the storage developer, the channel partner or the group developing management tools, that sort of thing, that's where we're going to offer some things to that development community, the people developing new storage widgets and apps and tools. And that's where the Dell Storage API comes in. We really view that as somewhat different than the business application audience. Okay, I wanted to switch gears a little bit and ask you about just as this capacity's increased, you know, mammoth sizes, you know, data on an actuator gets bigger, you know, performance is an issue, but there's also the issue of rebuild times, you know, raid rebuild times, raid five and then we have raid six and even during a long raid six rebuild, there's exposure. And so a number of companies are talking about erasure coding as a way around that. Do you have any thoughts on that?  So maximum efficiency is one of the tenets of fluid data Dell is really investing in being the best in storage at translating a certain amount of actual logical data into how much physical space that takes. And there is no one right answer for that because you have to define at the customer level how much protection you want, right? What are you protecting against? So things like compression and D-dupe and thin provisioning all play into this. We view erasure coding as one of the most important aspects of this going forward. And, you know, in a sense raid five and raid six are examples of erasure coding, but just for a specific failure case where you're encoding data to protect against the loss of a disk drive. But erasure coding in general allows you much more flexibility in what you're protecting against. You could turn the knob to say, well, I'm protecting against disk failure, or enclosure failure, or rack failure, or site failure, or citywide disaster. And mathematically, then a good erasure coding system will figure out how much parity, how many copies, where they need to be distributed to geographically to protect against the scenario that you want protected. And we really think that's where it's going. We think there's a lot of opportunity for real differentiation at the math, at the actual mathematics used to figure this sort of stuff out.  But what we want to be able to give people is basically a big knob that goes to 11. If you want to protect against everything, you'll be able to turn the knob there and get the most efficient possible space utilization for that level of protection. And that instance, throat core is at the problem, right? That's right. And given that it's so math heavy. So now is that something that's part of the portfolio today? Is that a potential future acquisition? Is that invention? It's a little of all those things. We do have erasure coding shipping in our scale out object store, the Dell DX object platform. But you could expect to see erasure coding propagating out through all the platforms over time. This is an area where, again, we want to see a Dell personality emerge. And you'll see that knob, you know, that you get to set be a consistent thing across the portfolio. So Carter, my last question for you, we're running out of time here is, how do you define leadership and what makes Dell a leader in storage? Well, we have in fluid data, a core set of tenants, the things that we think are really important in storage going forward. And those tenants align where we're investing in. And, you know, you could measure revenue or market share, those sort of things. We think those are sort of after the fact measures. But we want to be as clear thought leaders in the technology, in those six or seven areas that we've identified. Excellent. Carter George, thanks very much for taking some time out coming on the Cube. Great vision, great visionary. Good luck with the with the strategy and the rest of the show. Thank you very much. All right, keep it right there. We'll be right back with more coverage live from the Dell Storage Forum 2012 live from Boston. This is SiliconANGLE TV's The Cube. Keep it right there.


Hello and welcome to the Grand Line Review, your source for everything One Piece, and today we are going to get a bit controversial, or at least as controversial as a channel based around one, particular anime among can be, which we are going to be achieving by airing some unpopular opinions about One Piece. But there is a twist here because here's the thing, after making close to 700 videos based solely on One Piece, which, wow, that's a lot, I'm fairly certain that all of my unpopular opinions have already well and truly been aired. Some even on multiple occasions to you the long-suffering Grand Fleet. So in this particular instance, I have decided to give all of you the floor to state your own unpopular opinions, and I'm just going to sit here and judge you for them, which is of course a joke mostly. So let's jump straight into things with our first unpopular opinion, which is, Ace's death was overrated. This may be because I was spoiled about all of Marine Ford, but it didn't have an impact on me. So I feel like you're definitely not alone in this. The really weird thing about Ace is that for such a startlingly popular character, we really didn't actually get to know him until well after he died. All he had was that brief interaction on alabaster, a comical cover story, and then he spent most of his time in chains. So I completely understand not being able to really connect with the character at the point of his death anyway. However, I think what really sells it for most people isn't so much the sympathy towards Ace, but the empathy with Luffy. When Ace died, it kind of put me into a state of narrative shock more so than sadness because I just couldn't believe that this thing had happened in One Piece. But when I saw Luffy, that's what made the event emotionally impactful. Seeing our strong, infinitely optimistic protagonist fall apart like never before and never since. But look all in all, despite being one of the most important deaths in the series, I think that in the grand scheme of things, almost every other case of death is sadder than that of Ace. Usopp's fights are the best in the series. All right, might disagree, but hey, that's the nature of holding unpopular opinions. Still, let's try and get into the mind of this grand fleet member. And I think this argument could hold quite a lot of merit. Usopp and his fights probably get written off a lot because quite frankly, he doesn't have anywhere near enough of them. And when he does, they're always against these less than noteworthy opponents.  Four and Miss Merry Christmas on Alabasta and Pirona on Thriller Bark. So with the exception of Pirona, they all tend to be like the leftovers of the antagonistic crew. So there's not a lot of innate hype in seeing him take them on. However, despite the rarity and the riffraff he has to work with, these fights are all pretty incredible when you think about it.  With Chu, he proves to himself that he can defeat opponents stronger than him. On Alabasta, he fights for the pride of his captain, abandoning all of his selfishness for the first time in the series. And on Thriller Bark, he overcomes so much just to beat Pirona. And you know what, how's this? I didn't even think of Luffy versus Usopp actually. So while Usopp really doesn't fight all that much, they're all pretty groundbreaking events. So you know, I disagreed at first but I'm slowly coming around to this idea of Usopp's fights being the best in the series. Unpopular opinion. The subscribe button is harder to hit than Khadakuri. All right, let's meet this with a popular opinion. The subscribe button is easy to hit, just not by you. So I want all of you right now who have not yet subscribed to show this full what's what by casually pressing that beautiful, gorgeous red button and becoming members of the Grand Fleet which will result in regular lumpy's content being uploaded straight into your YouTube feed. And really never before in your life have you been asked to do so little in order to gain so much. But moving on. Chopper developed into a boring mascot character. And I don't like the sentiment of this opinion but in the post-timeskip era, it's quite hard to argue with.  But Chopper really seems to have conquered all of that off-screen during the timeskip. And after that, he doesn't really have any inner turmoil anymore. So he does just kind of sit there and look cute. Which to be fair is what he does best. So I'm not complaining. Sanji is stronger than most of the supernovas. Ah, power scaling, eh? I mean, maybe. It's very hard to tell, but I suppose that by virtue of that statement that kind of maybe makes it true. And you know what? Why shouldn't it be? He isn't a supernova or a member of the worst generation. They're different things. But we all know he was a powerhouse during the Saapiti day as it just took him a lot longer to get recognized. Still, I don't know. There's a whole ton of them that I don't see Sanji topping in terms of strength, like, say, Rouge. Then there's ones where he has horrible, horrible matchups of power, like Lore. And somewhere he would almost certainly come out on top like Capone, but there's just too many question marks. All I'll say is that I don't care if he is. It makes sense that he is as strong, if not stronger than most of them. So, meh. The manga has gone downhill in terms of paneling.  There seems to be no good close-ups of characters anymore. And this is an interesting discussion, actually. I find myself on the very opposite end of the spectrum, though. I really love the small panels, and I think they used quite masterfully to compress incredible amounts of information into a weekly 18-page product. Without this choice in play, I just don't think we'd be able to tell the story, at least not without another, I don't know, 1,000 chapters. So, no, it's not what One Piece used to be, but at the same time, One Piece used to be a boy in a dinghy. The story and the world have grown ever so slightly more complex since then, and I think the paneling very well reflects that. Oda has built up the One Piece for far too long. But there to possibly be a physical object that could ever live up to be the treasure they find. And so the only suitable way to win the series would be a friends-on-the-way style of reward, rather than a physical object. Lots of agree here, and yet, lots of disagree. I do think that this 23-year mystery is going to be nigh on impossible to solve without disappointing probably a lot of people after this kind of historic build-up. That's just the nature of mysteries in general, though. Solving them is almost never satisfying beyond the initial shock of the moment in which you do. And it's because it gives our brains permission to stop thinking, which is very disengaging, obviously. However, the One Piece is definitely not going to be along the friendship lines or any of that crap. Oda has confirmed that the One Piece is indeed a tangible thing, and regardless of how satisfying it is, that's what we're gonna get. And also, I don't think the series is going to end with finding the One Piece. Rather finding the One Piece is probably going to trigger the end events of the series.   Dude is a monster. Yeah, Hachan is a bit of a tough one. Although look, the whole map thing wasn't him intentionally targeting and enslaving Nami. It's more like a derpy octopus who found some paper and went, who maps? But looking back on Hachan, he's responsible for a hell of a lot of pain, even if he wasn't the one directly inflicting it. He was still facilitating it and quite willingly at that. It's not as if he didn't know who Arlong was and what he was doing.  So that's why that whole scene on Sabati when Nami is eating his takoyaki always hits me so hard. Hachan is a lovable guy in general, but there's no excusing his actions or inactions. And I don't know, he's trying, he feels guilty. And I guess that Nami's moved past it. So, so can I. And so can we or not. Up to you. Pacing can be absolutely atrocious, especially post-timescape. Atrocious and not always worth it. Edit, anime and manga. All right, that second distinction is actually pretty important. I'm not going to address the anime here because look, I agree. And most of you know my many, many issues, but pacing with the manga, well, that's a fairly fresh discussion. And in my opinion, it can be great and it can be awful. Especially post-timescape with the advent of all the mega arcs. Dressroser is the obvious example, but more recently, the pacing of Act 2 of Wano started to get really quite grindy for me. But that's only from the perspective of reading weekly. And for example, when I reread Dressroser, I don't see any pacing issues whatsoever. I just enjoy a giant adventure, which is something that manga is really good at because it allows you to effectively set your own pacing. So if you think things are taking too long, then you just speed up reading. And if you think things are going too quickly, then you slow down. That's an advantage that the anime doesn't really have. But in the end, I guess, feeling the grind is just a harsh reality of reading or watching a mammoth series like this weekly. I like Frank's post-timescape design more than his pre-timescape. I'm assuming Frankie. If you're talking about Frank, let me know. But in regards to Frankie, yes, me too. I've never, ever, ever understood the people who hate on post-timescape Frankie. I love him. I love it so much that I find it really difficult to go back to arcs like any Slobby and see what he used to be because it just feels so underwhelming. But this is definitely an unpopular opinion. I know that there are a massive legion of pre-timescape Frankie fanatics, but here's the thing about that. No matter what those people say, we win because post-timescape Frankie is here to stay. Unpopular? I don't like Law that much and I think people treat him like a better character than he really is. And you know what? I actually kind of did a whole video on this. Law is the most popular non-straw hat character in the series according to official popularity polls. And I think that most people's anecdotal evidence would go on to suggest that as well. But that's what's going to happen when you have a sleekly designed brooding cool guy. It's a guaranteed formula for success. Under these circumstances, Law doesn't need to actually do anything to achieve mass popularity as I explored and proved in my video. However, after diving into his backstory, that is what has solidified him as an established pillar of One Piece popularity. And yeah, I don't quite see it myself. I like Law. I like Law a lot, but I like other characters more. The fights are easily the worst part of the series. Now this might seem like a controversial statement, but I don't disagree at all.  But that doesn't mean the fights are bad, very different. There are far too many people who conflate the words worst and bad. But seriously, the fights are by and large, pretty fantastic. However, when I compare them to everything else One Piece does, so incredibly right, then yeah, I guess by default, the fights do become technically the worst part of the series, which is amazing because if that is the worst thing that One Piece has to offer, then its best is going to be off the charts. Magellan is arguably capable of fighting with admirals. The man literally guards thousands of infamous criminals. Yeah, I guess, here's the thing, the statement, it isn't technically wrong. Magellan is capable of fighting with the admirals, so is Woopsap though. He's very capable. I just don't think it would go particularly well for him. Although when you think about it, Woopsap actually has the advantage of not being stuck on the toilet for the large majority of a day. So Magellan may do even worse in a fight against an admiral than Woopsap would with that in mind. I'm not a big fan of the no romance rule amongst straw hats. So just amongst the straw hats, I thought it was a general rule for One Piece. Actually, I guess there are one-sided exceptions like Boa Hancock and super rare couples like Capone and Chiffon, who are adorable, but those things are mostly played for comedy. And adding romance on top of everything that One Piece already needs to accomplish would extend this series into infinity. I mean, shippers gonna ship, but the reality of a romance story is needing to add turmoil. It's not like Luffy and Nami would just get together and stay that way for the rest of the series because when romance is an element, then it needs development, which means that we'll need to be constantly exploring, updating and even breaking relationships. And oh, it's just exhausting to think about it, which is probably why in non-romance focused stories that stuff always gets used as a full stop at the end of the series. You know, these people get together and live happily ever after. I think Mihawk isn't really cool. And the only thing making him interesting is that he is Zoro's final enemy, probably. This probably goes back to the law discussion. It's the standard outcome of creating a character whose aesthetic is just so sharp in a sea of mainly goofy figures. Mihawk also has the supreme advantage of status though. He holds the title of the world's greatest swordsman, which means that even if we never see him do anything ever, he still plays on the imagination. And all right, let's do one more unpopular opinion. Treble is a good character. You're wrong. But what do you guys think? Please do leave your thoughts in the comments below or even join my Discord server. And if you'd like to see more videos like this, then please do go and check out some of my other content or even subscribe to the channel for more glorious One Piece business uploaded straight until YouTube feeds. But for now, this has been the Grand Line Review and I'll see you next time.


How's it going everyone Caleb here with late in sports cards next night? We're gonna be working on tops tier one Full case break number 54 random team style. Thanks for joining. Good luck box there results there They're also linked in your chat. Here we go guys See if we can somehow top the last one although it will be tough It's possible though. See what we got and then we're right into definitive after this tonight Like geez The best of the best right now, we're hitting good guys. We're hitting good. Wow. It feels like a good one to start with The buck all Red Sox Dustin Petroia patch at 349 to 249 Adrian Beltray patch rangers It's not forced. Yeah, exactly exactly 39 of 299 for the Rangers Yoni Hernandez and Red Sox autographed 167 of 200 Mo Vong Yeah, go Dan Daniel W. That is move on continuing along guys Patch card here gonna be Braves Freddy Freeman to 299. What's going on here? Max Kepler to 299 for the Twins That's so wild It's a what wait a second one of one Oh The bet relic Wow That's a one of one Richard a How about that? Dude, that's fire wild So it's not a knob, but it is like a jumbo bat relic and then he signed right on it And it's a one of one What is this thing man, what is this thing right first? Yeah, I Was looking at it and we were both looking at it and then all of a sudden I saw the one of one I was like, okay, okay Yeah, that's really cool You go that's Richard a with the Mets Congrats, man So sick there Me me the forest me neither. So I was just like staring at it. Like what is this thick card? That's in the back It didn't make any sense at first That's fire That is fire To 299 Matt Chapman patch. What's up Mike? Hey Mike. Good to see you Autograph Jake McCarthy to 299 D-backs Of course, that'll be magged. I feel like all the hits were getting tonight like I don't need to say Just just gets magged Sam's well aware to 299 Fergie Jenkins cubs on the tier one talent auto there. They had him on the field of dreams game It was really cool. Yeah, I turn. Yeah, I remember that field of dreams game Me and I think he was me in forest breaking Her force is breaking. I was top-loading and that that was a fun one to watch That walkoff was just it was exactly what it's not that cool Let's hit the brakes Brewers patched at 399 Corbin burns. I always forget that Sam's a Yankees fan. Yeah, until it's too late You go brewers. Oh nice. Silver ink autographs, sunny gray for the red six up 10 Yankee light right Mike, sunny gray Yankee legend. I think so the field of dreams game forest Last year's when Tim Anderson hit the walkoff And DJ LeMay he won the auto 103 of 299 for the Yankees that game was so cool Yep, guys, that's the only break with spots left tonight. It's top spin is Star Wars random mini box style It has 14 to go remember with each spot purchase your guarantee an entire mini box Which is one hit and then usually a color or two. So check it out guys Check it out. It's linked right there in the chat for you. That's the only break with spots left this evening You tweet that as well We did Into 399 on the patch Torrey Hunter Tigers Yeah, that was that was so cool as well forced we opened this crazy luminaries case Oh, yeah, that honus Wagner. I sent the picture. Oh, yeah. Yeah. Yeah. That was so cool as well Patrick Wisdom 292 of 299 cubs. I would have been to be a fly on the wall Yeah, that card was just awesome Cubs we were both just freaking out Austin Riley 63 of 299 on the auto their Braves One of the coolest cuts you could pull The baseball card himself The baseball card. Oh my god, the red sock boom Dan W Awesome Rafi devours.   What's up, Elias? Wow Mag that Jake Myers to 299 on the rookie auto Holy cow Dude What's up, man? Not too much 109 to 199 seven or Perez auto for the Royals nice Just pulling huge cards left and right. That's all That is all no big deal second half Forrest is still not over it. Oh My goodness make for us might have done IRL back flip right there for us Dan might make that card Well, let's go Dan Dan's in shot. Let's go. Let's go Dan. You know me him and as their white socks to 299 Dan if you do make that card available make sure you message me. I can get in contact with Forrest See if he wants it Royals there Emmanuel Rivera to 299 rookie auto. Oh, I will I will don't worry You got Royals and if you keep it Dan, I totally understand.  Yes Arguably my favorite Photograph and all sports can actually see you what his name is You could have no name played here. You'd be able to tell what it is You don't even need the picture on there, honestly Here we go Yeah, Dan selected with what he keeps for sure. Yeah, that's why I mentioned it To 399 47 to 399 Kyle Tucker nice one Astros You've got at least hold it though first in 181 of 299 Ryan Velaid Rockies This one Rockies on the rookie auto And Blake Snell 124 of 199 auto their Padres Yeah, go Let's keep going Let's keep it going I want to I want to these cards are fire We're pulling fire cards labor Torres to 399 Yankees on the patch Colton Welker rookie autograph Rockies It's just like I mean in terms of a Red Sox patch. That's the one they have, you know You have to have a sock patch And Brandon Crawford there nine of 299 for the Giants That's what I mean, it's just like there's just something about patches like that Me and Sam we're talking about yeah, we're literally having that exact conversation just some teams just it doesn't player doesn't matter at all just The patch patches there Garrett called the 399 Yankees And Brandon belt to 399 their Giants 251 of 299 Cardinals rookie autograph of Lars new bar. It's like a little bit thicker for whatever reason No idea why I did bring it fixly just you know and Mark McQuire auto 2950 that's cool as well Cardinals. I like that Design Yeah, it was just a couple to go guys Two boxes remaining. That's what I'm saying force. We haven't really missed yet If this can continue man As we get into these big products that would just be fantastic To 399 Gary Sanchez Yankees I'm scared to 399 code or excuse me to 299 Cody Beltinger Dodgers been better 15 to 299 I grabbed this time 203 of 299 Tyler Gilbert's And another hit for the Red Sox this time 27 of 299 Jim Rice Another Red Sox it Had a great break last box here Gravy there Dan yeah Joe Safety belt To 399 Orioles Cedric wall and spatch pirate saw to grab three of 299 Brian Reynolds And we're closing out to your one today last one here with a Ernie Clement autograph. That's guardians 14 of 299 On the rookie auto there guys. Thank you so much for joining another insane case It's your one definitely two for two on those tonight Let's do a recap here and we'll be out of the definitive Definitely two for two on those though. That was sick Pash cards here Cedric Mullins Orioles Cody Beltinger Dodgers Gary Sanchez Yankees Brandon Bell Giants Garrett Cole Yankees labor Torres Kyle Tucker Astros Eli Jimenez White Sox Torrey Hunter Tigers Corbin Burns Brewers Matt Chapman athletics Freddie Freeman Braves Beltray for the Rangers Dustin Pedroia Red Sox and the Red Sox the Red Sox Oh Man Raffi Deppers on that one of one guys Okay, we've got autographs now guardians Ernie Clements Pirates Brian Reynolds Red Sox Jim Rice Tyler Gilbert's d-backs Mark McGuire cardinals Lars Newport cardinals And Crawford for the Giants Colton Welker Rockies like snow Padres Ryan delayed Rockies Ozzy Smith cardinals a Manuel Rivera Royals Jake Myers Astros the one for the Royals Salvador Perez Austin Riley Braves Patrick Wisdom Cubs DJ Lemay who Yankees Sonny Gray Reds Fergie Jenkins Cubs Jake McCarthy d-backs Max Kepler twins mobile on Red Sox and Yoni Hernandez for the Rangers And then we also had this sick bat relic jumbo autograph Peter Lonzo for the match that is a one-of-one So a couple are really really unique one-of-ones and that's here one guys. So thanks again so much for joining appreciate it We'll have them all well protected in right out to you


So one important thing to keep in mind about doing mathematics is not to get lost in the pushing symbols around odd paper, but to remember why you're doing what you're doing. And this is particularly true in, well, everything, but we'll just as an example take a look at this in terms of rational expressions. So again, let's consider the problem simplifying this rational expression. And so first of all, the one thing you should absolutely always do is find the forbidden values that will make the denominator equal to zero. And again, the reason that you're doing this is if the denominator is ever equal to zero, this expression is meaningless. So we'll go ahead and solve for those. And that's a nice quadratic equation. And we can solve that and you find x equals three x equals negative two are the roots that will make the denominator equal to zero. So I can factor the denominator into x minus three times x minus negative two x plus two. So our denominator factors nicely. Now our next step in general is to try and simplify the numerator by factoring it. And while you might note that this is a cubic equation x to the third, so we don't have any nice quadratic formula to solve for it. So we fall back on the rational root theorem and the rational zero theorem and our solutions are going to be divisors of 12 divided by divisors of 6. And unfortunately, that's a lot of numbers. Divisors of 12 include 1, 2, 3, 4, 6, and 12. Divisors of 6 include 1, 2, and 3. So I'm going to have lots and lots and lots and lots and lots and lots of potential factors. And that's a lot of work even though we do have a fast way of doing that. So here's an important question to ask. We could factor the numerator. Why? And the reason is that factoring is only going to be useful if we're going to be able to cancel a factor from the numerator with a factor in the denominator. And, well, there's only two factors in the denominator, which means that if I factor the numerator and I don't get at least one of these, all that effort in factoring the numerator is wasted. I can't do anything useful with it. So what we really care about, what is really important here is, is x minus 3 a factor of the numerator? Or is x plus 2 a factor of the numerator? And so I can determine not whether the denominator factors, but whether its factors include x minus 3 or x plus 2. So I can answer this question directly using the factor theorem. If x equals 3 makes the polynomial, makes our numerator equal to 0, then x minus 3 is a factor. And conversely, if x equals 3 does not make this numerator 0, then x minus 3 is not a factor, and I don't have to worry about it. I'll use synthetic division in the remainder theorem to evaluate our polynomial at x equals 3. So I'll set up my synthetic division table. So again, the value I'm testing is x equals 3, my coefficients, 6x cubed, 3x squared, minus 24x, minus 12 is my constant, and I'll apply the synthetic division algorithm. I'll drop, multiply, add, multiply, add, and, well, a little analysis goes a long way.  But when I add that to negative 12, what I really care about is whether or not I get 0. Well, 39 times 3 added to negative 12. Well, 39 is already bigger than 12. So times 3, I'm a lot bigger than 12. So if I add it to negative 12, what I get here is not going to be 0. So who cares what that product is? It's not going to give us 0 at the end of it. I don't actually need to finish the synthetic division algorithm. What I do know is that x equals 3 does not make my polynomial equal to 0. So I know that x minus 3 is not a factor. Well, let's check the other factor of significance, this x plus 2. And so I can check to see if x plus 2 is a factor. If x equals negative 2 makes the polynomial equal to 0, then x plus 2 is a factor. Otherwise, it isn't. So I'll set up my synthetic division table. So I'll drop, multiply, add, multiply, add, multiply, add. And at the end of it, I have a 0, which tells me that x equals negative 2 makes the polynomial 0, which means that x minus negative 2, x plus 2 is one factor of this numerator. And that gives me a factor. Now the other factor is going to be what I got from the synthetic division. So I also have the other factor. And now I have a common factor I can cancel out. There it goes. And I have another expression. Now we've already determined x minus 3 is not a factor of the numerator, which means that I can't simplify this expression any further. However, just to dot all your i's and cross all your t's, you may want to indicate this just to make everybody happy. You should actually point out that you're not going any further because it's not worth it and not because you decided you wanted to quit the problem at this point. So it's worth making a point of saying that x minus 3 is not a factor of the numerator. So I can't actually simplify this expression any further.


We know that it's hard to stay up to date on USIP's latest publications, so we've challenged our teams to summarize their latest research in less than a minute. This is briefly. Over the last year, the US Institute of Peace convened a bipartisan senior study group composed of nine former US officials with decades of expertise in diplomacy, defense and security policy, and humanitarian and development assistance to reconsider US policy in the Red Sea arena. The group determined that while the Horn of Africa has been fundamentally reshaped in recent years and is now an integral part of the security systems of the Middle East, the broader Indian Ocean, and the Mediterranean, US strategy has struggled to keep pace. To address this gap, the study group has outlined a detailed policy blueprint to advance and defend US interests in this dynamic region based on four pillars. Number one, a political and diplomatic strategy to inoculate the Horn of Africa against the fallout of Middle Eastern rivalries. Number two, designation of either a special envoy or the deputy secretary of state to lead the development and execution of an integrated diplomatic strategy on the Red Sea arena. Number three, realignment of US assistance in the Red Sea arena to promote inclusive legitimate governance and economic growth. And number four, an active congressional engagement.