28 New SAT Math Lessons – Advanced Course

Last week I posted a question from my new book 28 New SAT Math Lessons – Advanced Course. Today I will provide a solution to that question. And now here is last week’s question with a solution.

Level 5 Passport to Advanced Math

For a polynomial p(x), the value of p(–3) is 5. Which of the following must be true about p(x) ?

(A) x – 8 is a factor of p(x).
(B) x + 5 is a factor of p(x).
(C) x – 5 is a factor of p(x).
(D) The remainder when p(x) is divided by x + 3 is 5.

This problem can be solved in just a few seconds if you know the remainder theorem. This theorem says that for a polynomial p, p(r) = a if and only if the remainder when p(x) is divided by x – r is a.

To apply the remainder theorem to this questions, since p(–3) = 5, by the remainder theorem , the remainder when p(x) is divided by x + 3 is 5, choice (D).

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