Answer
$-16(t+1)(t-5)$
Work Step by Step
Factoring the negative $GCF=
-16
,$ the given expression, $
-16t^2+64t+80
,$ is equivalent to
\begin{array}{l}\require{cancel}
-16(t^2-4t-5)
.\end{array}
The trinomial expression above has $c=
-5
$ and $b=
-4
.$
The possible factors of $c$ are $
\{ 1,-5 \}
,\{ -1,5 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
1,-5
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
-16(t+1)(t-5)
.\end{array}
