Question

select the correct answer.
what is the factored form of ( x^3 + 216 )?
a. ( (x - 6)(x^2 + 6x + 36) )
b. ( (x + 6)(x^2 - 6x + 36) )
c. ( (x + 6)(x^2 - 12x + 36) )
d. ( (x + 6)(x^2 + 12x + 36) )

Explanation:

Step1: Recall Sum of Cubes Formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).
Here, \(x^3+216=x^3 + 6^3\), so \(a = x\) and \(b = 6\).

Step2: Apply the Formula

Substitute \(a=x\) and \(b = 6\) into the sum of cubes formula:
\(x^3+6^3=(x + 6)(x^2-(x\times6)+6^2)=(x + 6)(x^2-6x + 36)\).

Answer:

B. \((x + 6)(x^2 - 6x + 36)\)