8
AssignmentMultiple Choice

Factoring Polynomials: Sum and Difference of Cubes

Question 8 • Common Core Algebra I B-IC

Factor 64 – x15.

Answer
A
(4 – x3)(16 + 4x3 + x3)
B
(4 – x3)(16 + 4x3 + x6)
C
(4 – x5)(16 + 4x5 + x5)
D
(4 – x5)(16 + 4x5 + x10)

Explanation

Rewrite 64 − x¹⁵ as 4³ − (x⁵)³. Using the difference-of-cubes rule, a³ − b³ = (a − b)(a² + ab + b²), with a = 4 and b = x⁵, gives (4 − x⁵)(16 + 4x⁵ + x¹⁰), which is choice D.

AI-written and checked against the verified answer.

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