Question

find the quadratic polynomial that completes the factorization.
$v^3 + 27 = (v + 3)(square)$

Explanation:

Step1: Identify sum of cubes

$v^3 + 27 = v^3 + 3^3$

Step2: Apply sum of cubes formula

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ where $a=v$, $b=3$

Step3: Substitute values

$(v + 3)(v^2 - v\cdot3 + 3^2) = (v + 3)(v^2 - 3v + 9)$

Answer:

$v^2 - 3v + 9$