PSAT Math Multiple-Choice Question 713: Answer and Explanation

Question: 713

What is the value of the constant c in the equation below?

(x - 6)(x - 10) = (x - 8)² + c

• A. -4
• B. 0
• C. 4
• D. 16

Correct Answer: A

Explanation:

(A) Use FOIL on both sides to get:

x² - 16x + 60 = x² - 16x + 64 + c

The coefficients of like terms of both sides of the equation must equal one another. The coefficients of the x²-terms and of the x-terms are already equal on both sides. However, the constant terms must equal one another as well:

60 = 64 + c

Subtract 64 from both sides:

-4 = c

Choice (A) is correct.