PSAT Math Multiple-Choice Question 435: Answer and Explanation

Question: 435

If x² + 8x = 48 and x > 0, what is the value of x - 5?

• A. -9
• B. -1
• C. 4
• D. 7

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Solving Quadratics by Factoring

Strategic Advice: When finding solutions to a quadratic equation, always start by rewriting the equation to make it equal to 0 (unless both sides of the equation are already perfect squares). Then, take a peek at the answer choices—if they are all integers that are easy to work with, then factoring is probably the quickest method for solving the equation. If the answers include messy fractions or square roots, then using the quadratic formula may be a better choice.

Getting to the Answer: To make the equation equal to 0, subtract 48 from both sides to get x² + 8x - 48 = 0. The answer choices are all integers, so factor the equation. Look for two numbers whose product is -48 and whose sum is 8. The two numbers are - 4 and 12, so the factors are (x - 4) and (x + 12). Set each factor equal to 0 and solve to find that x = 4 and x = -12. The question states that x > 0, so x must equal 4. Before selecting an answer, don't forget to check that you answered the right question—the question asks for the value of x - 5, not just x, so the correct answer is 4 - 5 = -1. (B) is correct.