Question

find the quadratic polynomial that completes the factorization.
$y^3 - 27 = (y - 3)(\square)$

Explanation:

Step1: Recall difference of cubes formula

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

Step2: Identify a and b

$a = y$, $b = 3$ (since $3^3 = 27$)

Step3: Compute quadratic term

$a^2 + ab + b^2 = y^2 + (y)(3) + 3^2 = y^2 + 3y + 9$

Answer:

$y^2 + 3y + 9$