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.)

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 to get to C and D? Well, by using the difference of two squares again, even though 3 isn’t really a square.