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: Recognize sum of cubes

$x^3 + 8 = x^3 + 2^3$

Step2: Apply sum of cubes formula

Recall $a^3+b^3=(a+b)(a^2-ab+b^2)$. Here $a=x$, $b=2$.
$$x^3+2^3=(x+2)(x^2 - x\cdot2 + 2^2)$$

Step3: Simplify the second factor

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

Answer:

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