4
AssignmentMultiple Choice

Factoring Polynomials: Difference of Squares

Question 4 • FL-1200700-Mathematics for College Algebra MIS

What is the factored form of 125x6 – 8?

Answer
A
(5x2 – 2)(25x4 – 10x2 – 4)
B
(5x2 – 2)(25x4 – 10x2 + 4)
C
(5x2 – 2)(25x4 + 10x2 + 4)
D
(5x2 – 2)(25x4 + 10x2 – 4)

Explanation

Recognize 125x6 – 8 as a difference of cubes: 125x6 = (5x2)^3 and 8 = 2^3. Using a^3 – b^3 = (a – b)(a^2 + ab + b^2), with a = 5x2 and b = 2, gives (5x2 – 2)(25x4 + 10x2 + 4), which is choice C.

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