Answer
$20y(x-2)(x-3)$
Work Step by Step
Factoring the $GCF=
20y
,$ the given expression, $
20x^2y-100xy+120y
,$ is equivalent to
\begin{array}{l}\require{cancel}
20y(x^2-5x+6)
.\end{array}
The trinomial expression above has $c=
6
$ and $b=
-5
.$
The possible factors of $c$ are $
\{ 1,6 \}
,\{ 2,3 \}
,\{ -1,-6 \}
,\{ -2,-3 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-2,-3
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
20y(x-2)(x-3)
.\end{array}
