PSAT Math Multiple-Choice Question 51: Answer and Explanation

Question: 51

Which of the following equivalent forms of the equation x² + 8x + 15 = 0 would be the most useful for finding the x-intercepts of the equation?

• A. x(x) + 8(x) + 15 = 0
• B. x² + 3x + 5x + 15 = 0
• C. (x + 3)(x + 5) = 0
• D. x² + 8x + 4 + 11 = 0

Correct Answer: C

Explanation:

C

The question asks for a certain form of the equation. There are many forms in which a quadratic can be written. To see x-intercepts or solutions, a quadratic must be in factored form, since factoring is used to find solutions. The factored form is y = a(x - m)(x - n), where m and n are the x-intercepts. Only (C) is in this form. The correct answer is (C).