PSAT Math Multiple-Choice Question 688: Answer and Explanation

Question: 688

Based on the graph of f(x) below, f(x) is divisible by which of the following expressions?

I. x - 4

II. x + 1

III. x + 3

• A. I and II only
• B. I and III only
• C. All of the above
• D. None of the above

Correct Answer: B

Explanation:

(B) From the graph, the function has zeros at x = -3 and at x = 4.

Starting with the x = -3, add 3 to both sides:

x + 3 = 0

Therefore, x + 3 is a factor. This means that the function must be divisible by x + 3.

Similarly, x = 4, so:

x - 4 = 0

Therefore, x - 4 is a factor of the function, meaning the function is divisible by x - 4. These are the only two zeros. So the function has only two distinct factors, which we have already found. Therefore, Options I and III are correct, which is choice (B).