4
QuizMultiple Choice

Factoring Polynomials Completely

Question 4 • Common Core Algebra I B-IC

Which product of prime polynomials is equivalent to 8x3 – 2x?

Answer
A
x(2x – 1)(2x – 1)
B
2x(x + 1)(x – 1)
C
2x2(2x + 1)(2x – 1)
D
2x(2x + 1)(2x – 1)

Explanation

First factor out the greatest common factor, 2x: 8x³ − 2x = 2x(4x² − 1). The expression in parentheses is a difference of squares, so 4x² − 1 = (2x + 1)(2x − 1). Thus the product is 2x(2x + 1)(2x − 1), choice D.

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