Answer
$5(t-2)(t+1)$
Work Step by Step
Factoring the $\text{GCF}=
5
,$ the given expression is equivalent to
\begin{align*}
5(t^2-t-2)
\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c=
-2
$ and $b=
-1
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-2,1
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
5(t-2)(t+1)
\end{align*}
