Question

Factor: 8+ x3

A(2+x)(4-2x+x2)

B (2+x)3

C(2-x)(4+2x+x2)

(2+x)(4+x2)

a2+2ab+b2 =(a+b)2

a2-2ab+b2 =(a-b)2

a3+b3 =(a+b)(a2-ab+b2)

a3-b3 =(a-b)(a2+ab+b2)

Answer 1

8 + x^3 = 2^3 + x^3, a sum of cubes. Using a^3 + b^3 = (a + b)(a^2 − ab + b^2) with a = 2, b = x gives

8 + x^3 = (2 + x)(4 − 2x + x^2).

This is option A (equivalently written (x+2)(x^2 − 2x + 4)).