perplexus.info :: Just Math : 16 choices

16 choices (Posted on 2019-01-21)

For a polynomial p(x), the value of p(3) is −2.

Which of the following must be true about p(x)?
A) x−5 is a factor of p(x).
B) x−2 is a factor of p(x).
C) x+2 is a factor of p(x).
D) The remainder when p(x) is divided by x−3 is −2.

Source: SAT

No Solution Yet Submitted by Ady TZIDON

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Solution

| Comment 1 of 5

D is true from the polynomial remainder theorem.

p(x) = x^2 - 11 satisfies the requirement of p(3) = -2. However none of x-5, x-2, or x+2 are factors of x^2-11. Therefore none of A, B, or C must be true.

Posted by Brian Smith on 2019-01-21 23:33:09

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