PSAT Math Multiple-Choice Question 777: Answer and Explanation

Question: 777

Which of the following is a solution to the equation below?
(x - 3)² -81 = 0

• A. 12
• B. 11
• C. 9
• D. 8

Correct Answer: F

Explanation:

(A) First, use FOIL for the (x - 3)2 term in the equation to obtain:
x² - 6x + 9 - 81 = 0
Then you can combine like terms:
x² - 6x - 72 = 0
This factors to:
(x - 12)(x + 6) = 0
Setting each term equal to 0 tells you that x can equal either 12 or -6. Only 12 is an option, so choice (A) is correct.