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Factoring Polynomials: Sum and Difference of Cubes

Question 1 • Common Core Algebra I B-IC

Which are perfect cubes? Check all that apply.

Answer
A
64
B
x16
C
8x3
D
27x4
E
81x6
F
125x9

Explanation

A monomial is a perfect cube when its numerical coefficient is a perfect cube and each variable’s exponent is divisible by 3. Here, 64 = 4³, 8x³ = (2x)³, and 125x⁹ = (5x³)³. The other choices fail one of these tests: their coefficients or exponents are not perfect-cube factors.

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