Tuesday, February 10, 2009

Algebra 2: Factoring Trinomials (Part 1)


Lesson 5 (Factoring Trinomials 1)
Puzzle (doc / pdf)



Daniel Springer said...

here is a really simple way to "factor" trinomials (or solve them).

Consider: x^2+9x-22=0
This says,
a pair of numbers differ by 9 and have a product of 22.

The two pairs that work are:
{9 and 11} and their opposites {-9 and 11}

We take the smaller of each pair since x is smaller than x + 9

Thus, x = 9 or -11.

The method really shines when the quadratic coefficient is not 1.


By mult. by 6 and factoring we write..
-->differ by 7, product = 30
pairs are {10 and 3} and {-10 and -3)
6x is larger than 6x-7-->we take the larger.

x = 10/6 or -3/6

We divided by 6, since the pair represented 6x, not 6

Nick said...

Dan - I'm pretty sure I've at some point decided that you use grapher to make your visuals. Like the little summary images you include with most posts - is that correct? They often look great. I can't get something as simple/nice in geogebra, and PSTricks is often the looooooooooooong way.

Dan Greene said...

Yep, Grapher it is. It can be a bit of a pain to work with in certain ways, but it usually makes nice images.

Nick said...

Is it just me or are there a few typos here... A few minutes later, I think it's just me. Well... I'm gonna give the puzzle a go, I'll report back on how it fares - thanks for offering it up.

Dan Greene said...

Nick, if you find any typos, please let me know, and I'll fix them right away. I hope the puzzle goes well for you.

DWees said...


See my algebra puzzle generator.