Answer
$x^2(x-10)(x-12)$
Work Step by Step
Factoring the $GCF=
x^2
,$ the given expression, $
x^4-22x^3+120x^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2(x^2-22x+120)
.\end{array}
The trinomial expression above has $c=
120
$ and $b=
-22
.$
The possible factors of $c$ are $
\{ 1,120 \}
,\{ 2,60 \}
,\{ 3,40 \}
,\{ 4,30 \}
,\{ 5,24 \}
,\{ 6,20 \}
,\{ 8,15 \}
,\{ 10,12 \}
,\{ -1,-120 \}
,\{ -2,-60 \}
,\{ -3,-40 \}
,\{ -4,-30 \}
,\{ -5,-24 \}
,\{ -6,-20 \}
,\{ -8,-15 \}
,\{ -10,-12 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-10,-12
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
x^2(x-10)(x-12)
.\end{array}
