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 sum of cubes

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

Step2: Apply sum of cubes formula

Sum of cubes: $a^3+b^3=(a+b)(a^2-ab+b^2)$
Here $a=x$, $b=2$, so:
$$x^3+2^3=(x+2)(x^2 - x\cdot2 + 2^2)$$

Step3: Simplify the second factor

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

Answer:

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