PSAT Math Multiple-Choice Question 524: Answer and Explanation

Question: 524

Which of the following is equivalent to the expression 3c² – 10c + 8?

• A. (3c – 4)(c – 2)
• B. (3c + 4)(c – 2)
• C. (3c – 8)(c + 1)
• D. (3c + 8)(c + 1)

Correct Answer: A

Explanation:

A

The question asks for an equivalent form of an expression. There is a variable in the answer choices, so plug in. Make c = 2. The expression becomes 3(2)² – 10(2) + 8 = 3(4) – 20 + 8 = 12 – 20 + 8 = 0. This is the target value; circle it. Now plug c = 2 into the answer choices to see which one matches the target value. Choice (A) becomes [3(2) – 4][(2) – 2] = (2)(0) = 0. This matches the target value, so keep (A) for now, but check the remaining answers just in case. Choice (B) becomes [3(2) + 4] [(2) – 2] = (10)(0) = 0. Keep (B) for now. Choice (C) becomes [3(2) – 8][(2) + 1] = (–2)(3) = –6. This is does not match the target value, so eliminate (C). Choice (D) becomes [3(2) + 8][(2) + 1] = (14)(3) = 42. Eliminate (D). Since two answers match the target value, choose a new value to plug in to the remaining answer choices. Make c = 3. The expression becomes 3(3)² – 10(3) + 8 = 3(9) – 30 + 8 = 27 – 30 + 8 = 5. This is the new target value; circle it. Choice (A) becomes [3(3) – 4][(3) – 2] = (5)(1) = 5. This matches the new target, so keep (A) for now. Choice (B) becomes [3(3) + 4][(3) – 2] = (13)(1) = 13. Eliminate (B). The correct answer is (A).