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AssignmentMultiple Choice

Factoring Polynomials: Sum and Difference of Cubes

Question 3 • Common Core Algebra I B-IC

The expression x3 – 64 can be written as (x)3 – (4)3. What is the factorization of x3 – 64?a3 – b3 = (a – b)(a2 + ab + b2)

Answer
A
(x – 4)(x2 + 4x + 8)
B
(x – 4)(x2 + 4x + 16)
C
(x – 64)(x2 + 64x + 16)
D
(x – 64)(x2 + 64x + 4,096)

Explanation

Use the difference-of-cubes rule: a³ − b³ = (a − b)(a² + ab + b²). Here a = x and b = 4, so x³ − 64 = (x − 4)(x² + 4x + 16). The correct choice is (x − 4)(x² + 4x + 16).

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