Factoring Polynomials Completely

Question 2 • AZ-Common Core Algebra II A

What is the factored form of x3 + 64?

Answer

(x2 + 8)(x + 8)

(x + 4)(x2 – 4x + 16)

(x – 4)(x2 + 4x + 16)

Recognize x3 + 64 as a sum of cubes: x³ + 4³. Use the identity a³ + b³ = (a + b)(a² − ab + b²), giving (x + 4)(x² − 4x + 16). This matches choice B.

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Sum and Difference of Two Cubes

Sum and Difference of Two Cubes

Synthetic Division and the Remainder Theorem