Question

find the quadratic polynomial that completes the factorization.
$x^3 + 64 = (x + 4)(quad)$

Explanation:

Step1: Recall the sum of cubes formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(a=x\) and \(b^3 = 64\), so we first find \(b\). Since \(4^3=64\), then \(b = 4\).

Step2: Apply the formula to \(x^3+64\)

Using the sum of cubes formula with \(a = x\) and \(b=4\), we have \(x^3+4^3=(x + 4)(x^2-(x)(4)+4^2)\).
Simplify the second factor: \(x^2-4x + 16\).

Answer:

\(x^{2}-4x + 16\)