SAT Math Multiple Choice Question 650: Answer and Explanation

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Question: 650

5. a4 - 6a2 + 10

Which of the following is equivalent to the expression shown above?

  • A. (a2 - 2)(a2 - 5)
  • B. (a2 - 1)(a2 - 10)
  • C. (a2 + 3)2 + 1
  • D. (a2 - 3)2 + 1

Correct Answer: D

Explanation:

D

Advanced Mathematics (multiplying polynomials) EASY-MEDIUM

The simplest way to approach this problem is to "expand" the choices to see which one yields an expression that is equivalent to the original expression. You must remember how to FOIL (Chapter 9, Lesson 4) when multiplying two binomials:

(A) (a2 - 2)(a2 - 5) = a4 - 5a2 - 2a2 + 10 = a4 - 7a2 + 10

(Close, but no.)

(B) (a2 - 1)(a2 - 10) = a4 - 10a2 - 1a2 + 10 = a4 - 11a2 + 10

(Close, but no.)

(C) (a2 + 3)2 + 1 = a4 + 3a2 + 3a2 + 9 + 1 = a4 + 6a2 + 10

(Close, but no.)

(D) (a2 - 3)2 + 1 = a4 - 3a2 - 3a2 + 9 + 1 = a4 - 6a2 + 10

(Yes.)

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