PSAT Math Multiple-Choice Question 96: Answer and Explanation

Question: 96

Which of the following expressions is equivalent to (x + 2)(x - 5) - 18?

• A. (x - 4)(x + 7)
• B. x² - 3x - 8
• C. x² - 3x - 25
• D. (x - 7)(x + 4)

Correct Answer: D

Explanation:

D

The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make x = 2. The expression becomes (2 + 2)(2 - 5) - 18, which is (4)(-3) - 18. This becomes -12 - 18 or -30. This is the target value; circle it. Now plug x = 2 into the answer choices to see which one matches the target value. Choice (A) becomes (2 - 4)(2 + 7), which is (-2)(9) or -18. This does not match the target, so eliminate (A). Choice (B) becomes 2² - 3(2) - 8, which is 4 - 6 - 8 or -10. Eliminate (B). Choice (C) becomes 2² - 3(2) - 25, which is 4 - 6 - 25 or -27. Eliminate (C). Choice (D) becomes (2 - 7)(2 + 4), which is (-5)(6) or -30. This matches the target. The correct answer is (D).