Answer
$3(y+3)(y+5)$
Work Step by Step
Factoring the $GCF=
3
,$ the given expression, $
3y^2+24y+45
,$ is equivalent to
\begin{align*}
3(y^2+8y+15)
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c=
15
$ and $b=
8
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
3,5
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
3(y+3)(y+5)
.\end{align*}
