Question

find the quadratic polynomial that completes the factorization.
$r^3 - 64 = (r - 4)(\boxed{\quad})$

Explanation:

Step1: Recognize difference of cubes

Recall formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Step2: Match to given expression

Here, $a=r$, $b=4$ since $4^3=64$.

Step3: Substitute into formula

$r^3 - 4^3 = (r - 4)(r^2 + r\cdot4 + 4^2)$
Simplify: $r^3 - 64 = (r - 4)(r^2 + 4r + 16)$

Answer:

$r^2 + 4r + 16$