Question

the polynomial $x^3 + 8$ is equal to
$(x + 2)(x^2 - 2x + 4)$.
$(x - 2)(x^2 + 2x + 4)$.
$(x + 2)(x^2 - 2x + 8)$.
$(x - 2)(x^2 + 2x + 8)$.

Explanation:

Step1: Recall Sum of Cubes Formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).

Step2: Identify \(a\) and \(b\) in \(x^3 + 8\)

Here, \(a = x\) and \(b^3=8\), so \(b = 2\) (since \(2^3 = 8\)).

Step3: Apply the Formula

Substitute \(a = x\) and \(b = 2\) into the sum of cubes formula:
\(x^3+8=x^3 + 2^3=(x + 2)(x^2 - x\times2 + 2^2)=(x + 2)(x^2 - 2x + 4)\).

Answer:

A. \((x + 2)(x^2 - 2x + 4)\)