Question

find the quadratic polynomial that completes the factorization.
$4t^3 - 256 = 4(t - 4)(\square)$

Explanation:

Step1: Factor out the common term

$4t^3 - 256 = 4(t^3 - 64)$

Step2: Recognize difference of cubes

$t^3 - 64 = t^3 - 4^3$

Step3: Apply difference of cubes formula

$t^3 - 4^3 = (t - 4)(t^2 + 4t + 16)$

Step4: Substitute back

$4(t^3 - 64) = 4(t - 4)(t^2 + 4t + 16)$

Answer:

$t^2 + 4t + 16$