Hi Mike: I get tripped up by factoring Qs like this, especially “NOT” Qs… What’s the best way to solve this? Tks!
Factoring the polynomial x^12 -9 reveals a number of factors for the expression. Which of these is NOT one of the possible factors?

A) x^6 +3
B) x^6 -3
C) x^3 + √3
D) x^3 – √3
E) x – √3

I’m not sure that “NOT” questions are a real pattern of questions in official materials, so I wouldn’t worry too much about this, especially because the presence of 5 answer choices is an immediate giveaway that this is not a question designed for practice on the new SAT.

The way to go here, though, is to factor the difference of two squares multiple times. (The answer choices provide a clue that that’s what you need to do.)

    \begin{align*} &x^{12}-9\\ =&(x^6+3)(x^6-3) \end{align*}

That’s a start–it helps you eliminate choices A and B. From there, look again at the answer choices to guide you further. (Remember, answer choices are 100% part of the question! Use them!)

E looks a bit different than C and D, so I’m leaning that way. How can I factor (x^6+3)(x^6-3) to get to C and D? Well, by using the difference of two squares again, even though 3 isn’t really a square.

    \begin{align*} &(x^6+3)(x^6-3)\\ =&(x^6+3)(x^3+\sqrt{3})(x^3-\sqrt{3}) \end{align*}

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