Intermediate Algebra (6th Edition)

$-16t(t-9)(t+4)$
Step 1: Find the GCF of the polynomial, $-16t^{2}+80t+576$. The GCF is $-16$. Remove this from inside the parenthesis. $-16t^{2}+80t+576=-16(t^{2}-5t-36)$ Step 2: Factor $-16(t^{2}-5t-36)$. Find two integers with a product $-36$ and a sum $-5$. $-9$ and $4$ have a product of $-36$ and a sum of $5$. $-16(t^{2}-5t-36)=-16(t-9)(t+4)$. Distribute $-16$ to check your answer and make sure you have the original polynomial, $-16t^{2}+80t+576$.