PSAT Math Multiple-Choice Question 62: Answer and Explanation

Question: 62

In the equation x² + 24x + c = (x + 9)(x + p), c and p are constants. If the equation is true for all values of x, what is the value of c?

• A. 33
• B. 135
• C. 144
• D. 216

Correct Answer: B

Explanation:

B

The question asks for a value of the constant c in the given quadratic equation. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labeling the answers as c and starting with (B), 135. The equation becomes x² + 24x + 135 = (x + 9)(x + p). The left side of the equation is a quadratic in standard form, and the right side is a factored quadratic; this means that 135 from the left side of the equation would equal 9p once the right side was expanded to standard form. Divide 135 by 9 to get x² + 24x + 135 = (x + 9)(x + 15). Test whether this is the right answer by using FOIL to expand (x + 9)(x + 15) into x² + 15x + 9x + 135 = x² + 24x + 135. The middle term is 24x, which matches the value given on the left side, so stop here. The correct answer is (B).