SAT · Passport to Advanced Math · Polynomial expressions and factoring
Question sat-q-00075
Medium Multiple choice No calculator
The question
The polynomial p(x) has p(-2) = 0. Which of the following must be a factor of p(x)?
- (x + 2)
- (x − 2)
- -2
- x
Show answer & worked solution
Answer: (x + 2)
Worked solution. By the Factor Theorem, p(a) = 0 if and only if (x − a) is a factor of p(x). Here a = -2, so the factor is (x + 2).
Why each wrong choice is wrong. The most common trap is the sign-flipped factor — students who memorize 'if a is a zero, then (x + a) is a factor' get this wrong every time.
Test-day tactic. Factor Theorem in one line: zero at a → factor of (x − a). The sign matches the sign of subtraction, not the sign of the zero itself.
About this question type
Polynomial items test the relationship between the factored form and the zeros, end behavior, polynomial long division (rare), and the remainder theorem (occasionally). Most items reduce to either factoring a quadratic-shaped polynomial or recognizing that a polynomial has a factor of (x − a) when a is a zero.
You will see a question shaped like this one on roughly every other official SAT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.