PSAT Math Multiple-Choice Question 508: Answer and Explanation

Question: 508

In the expression x² + cx – 8, c is an integer. If the expression can be rewritten as the equivalent expression (x – c)(x + 4), which of the following is the value of c?

• A. 4
• B. 2
• C. –2
• D. –4

Correct Answer: B

Explanation:

B

The question asks for the value of c in two equivalent expressions. Since the question asks for a specific value and the answers contain numbers in decreasing order, plug in the answers. Begin by labeling the answers as "c" and start with (B), 2. The first expression becomes x² + 2x – 8 and the second expression becomes (x – 2)(x + 4). There are a few ways to determine if these expressions are equivalent. One is to use FOIL to multiply the binomials in the second expression, which results in x² + 4x – 2x – 8. This simplifies to x² + 2x – 8, which matches the original expression. Another method to check if the expressions are equivalent is to plug in a value for x, as the expressions should be true for any value of x. If x = 2, the first expression becomes 2² + 2(2) – 8 = 4 + 4 – 8 = 0. The second expression becomes (2 – 2)(2 + 4) = (0)(6) = 0. The expressions are equivalent. Either way, the correct answer is (B).