#### Answer

$(t-2)(t^2-5)$

#### Work Step by Step

Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
t^3-2t^2-5t+10
\\\\=
(t^3-2t^2)-(5t-10)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
(t^3-2t^2)-(5t-10)
\\\\=
t^2(t-2)-5(t-2)
.\end{array}
Factoring the $GCF=
(t-2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(t-2)(t^2-5)
.\end{array}