Answer
$t^2(t-2)(t^2+5)$
Work Step by Step
Factoring the $GCF=
t^2
$, then the given expression, $
t^5-2t^4+5t^3-10t^2
$ is equivalent to
\begin{array}{l}
t^2(t^3-2t^2+5t-10)
.\end{array}
Using factoring by grouping, the factored form of the expression, $
t^2(t^3-2t^2+5t-10)
,$
\begin{array}{l}
t^2[(t^3-2t^2)+(5t-10)]
\\\\=
t^2[t^2(t-2)+5(t-2)]
\\\\=
t^2[(t-2)(t^2+5)]
\\\\=
t^2(t-2)(t^2+5)
.\end{array}