Question

What is the factored form of the equation x³ - 64 = 0?

a) (x - 4)(x² + 4x + 16)
b) (x - 2)(x² + 2x + 4)
c) (x - 8)(x² + 8x + 64)
d) (x + 4)(x² - 4x + 16)

Answer 1

The factored form of x³ - 64 = 0 is (x - 8)(x² + 8x + 64), which represents the factoring of a difference of cubes.

Step-by-step explanation:

The factored form of the equation x³ - 64 = 0 is (x - 8)(x² + 8x + 64). This is because the equation is a difference of cubes, which can factored using the formula a³ - b³ = (a - b)(a² + ab + b²). In this case, a = x and b = 4, so when applying the formula we get (x - 4)(x² + 4x + 16), but since here we have 64, which is 4³, we need to use 8 which is 2³. Thus, the correct factored form is (x - 8)(x² + 8x + 64), which is choice c.