PSAT Math Multiple-Choice Question 666: Answer and Explanation

Question: 666

How many distinct zeros does the function f (x) = (x - 3)(x + 7)(x - 3) have?

• A. 0
• B. 1
• C. 2
• D. 3

Correct Answer: C

Explanation:

(C) The zeros of a factored polynomial can be found by setting each distinct factor equal to 0 and solving for x. Here there are only 2 distinct factors, (x - 3) and (x + 7). So there will only be 2, choice (C).

x - 3 = 0
x = 3
x + 7 = 0
x = -7

Note: Although x - 3 occurs twice as a factor, this still corresponds to only one zero. We say that 3 is a zero of multiplicity 2 since its corresponding factor occurs twice.