Answer
$x^2(x+2)(x-5)$
Work Step by Step
Factoring the $GCF=
x^2
,$ the given expression, $
x^4-3x^3-10x^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2(x^2-3x-10)
.\end{array}
The trinomial expression above has $c=
-10
$ and $b=
-3
.$
The possible factors of $c$ are $
\{ 1,-10 \}
,\{ 2,-5 \}
\{ -1,10 \}
,\{ -2,5 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
2,-5
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
x^2(x+2)(x-5)
.\end{array}