PSAT Math Multiple-Choice Question 813: Answer and Explanation

Question: 813

If -16 - 6x + x² = x² - abx - 8b, where a and b are constants, what is the value of a?

• A. -6
• B. -2
• C. 3
• D. 5

Correct Answer: C

Explanation:

(C) The different terms on the two sides of the equation equal each other. So -16 = -8b, -6x = -abx , and x² = x². Why? This occurs because the constants must equal each other, the terms with an x must equal each other, and the terms with an x² must equal one another. Since -16 = -8b, b = 2. Plug in 2 for b in the second equation and cancel out the -x to solve for a:

-6x = -abx → 6 = a · 2 → a = 3