Answer
$3(y-2)(y+3)$
Work Step by Step
Factoring the $GCF=
3
,$ the given expression, $
3y^2+3y-18
,$ is equivalent to
\begin{array}{l}\require{cancel}
3(y^2+y-6)
.\end{array}
The trinomial expression above has $c=
-6
$ and $b=
1
.$
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}
3(y-2)(y+3)
.\end{array}
