Question

find the quadratic polynomial that completes the factorization.
$t^4 - 512t = t(t - 8)(\quad)$

Explanation:

Step1: Factor out monomial from left side

$t^4 - 512t = t(t^3 - 512)$

Step2: Recognize difference of cubes

$t^3 - 512 = t^3 - 8^3$

Step3: Apply difference of cubes formula

$t^3 - 8^3 = (t - 8)(t^2 + 8t[Client Connection Error] + 8^2)$

Step4: Simplify and substitute back

$t(t^3 - 512) = t(t - 8)(t^2 + 8t + 64)$

Answer:

$t^2 + 8t + 64$