Question

If x + 4 is one factor of x3 + 64, what is the other factor?

Answer 1

`\Huge \boxed{(x^2 - 4x + 16)}`

Explanation:

x³ + 64

64 is a perfect cube. Rewrite 64 as 4³.

x³ + 4³

Apply sum of cubes formula:

• a³ + b³ = (a + b)(a² - ab + b²)

a = x

b = 4

(x + 4)(x² - (x)(4) + 4²)

(x + 4)(x² - 4x + 16)

(x² - 4x + 16) is the other factor.