PSAT Math Multiple-Choice Question 679: Answer and Explanation

Question: 679

Which of the following equations represents the function graphed above?

• A. x³ + 11x² + 36x + 36
• B. x³ - 11x² + 36x - 36
• C. x³ + x² - 24x + 36
• D. x² - 5x + 6

Correct Answer: B

Explanation:

(B) The function has zeros at 2, 3, and 6. We can use this to find the factors of the function.

If x = 2, x - 2 = 0. So (x - 2) is a factor.

If x = 3, x - 3 = 0. So (x - 3) is a factor.

If x = 6, x - 6 = 0. So (x - 6) is a factor.

Therefore, the function can be rewritten as y = (x - 2)(x - 3)(x - 6). All of the answer choices are in their unfactored forms, so use FOIL. Start by using FOIL with the first two-factors:

y = (x² - 5x + 6)(x - 6)

Then multiply the remaining factors:

y = x³ - 11x² + 36x - 36

This matches choice (B).