Hello! Do you think you could explain number 8 in the Polynomials Practice Questions of the PWN the SAT Math Guide 4th Edition? Thank you!

Gladly! I think the best way to go for this one is to factor.



From that, you can see pretty quickly that two answer choices aren’t right. First, you see that g(x) is most definitely a factor of f(x), so A isn’t the answer. You can also see that g(x) has two real zeros (–5 and 2), so C isn’t the answer.

You can also probably see what the answer is. Once everything is factored, it’s clear that (x-5) is not a factor of f(x). That means B is the answer.

As for D, well, once you know the answer is B you might not want to worry about it. But in case it’s keeping you up at night, here’s the deal. If h(x)=f(x)+2g(x), then we can use the factoring we’ve already done to write the following.


See how you can factor (x+5)(x-2) out of both terms?


That’s how you know that (3x+2) is a factor of h(x), which means you can cross off choice D.

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