Question

1. what is the factored form of $x^3 - 8$?

a. $(x - 2)(x^2 + 2x + 4)$
b. $(x + 2)(x^2 + 2x + 4)$
c. $(x + 2)(x^2 - 2x + 4)$
d. $(x - 2)(x^2 + 2x - 4)$

Explanation:

Step1: Identify difference of cubes

$x^3 - 8 = x^3 - 2^3$

Step2: Apply difference of cubes formula

Recall $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$
Substitute $a=x$, $b=2$:
$x^3 - 2^3 = (x - 2)(x^2 + (x)(2) + 2^2)$

Step3: Simplify the quadratic term

$(x - 2)(x^2 + 2x + 4)$

Answer:

a. $(x - 2)(x^2 + 2x + 4)$