Answer
$6(y+8)(y-5)$
Work Step by Step
Factoring the $GCF=
6
$, then the given expression, $
6y^2+18y-240
$ is equivalent to
\begin{array}{l}
6(y^2+3y-40)
.\end{array}
The two numbers whose product is $ac=
1(-40)=-40
$ and whose sum is $b=
3
$ are $\{
8,-5
\}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is
\begin{array}{l}
6(y^2+8y-5y-40)
\\\\=
6[(y^2+8y)-(5y+40)]
\\\\=
6[y(y+8)-5(y+8)]
\\\\=
6[(y+8)(y-5)]
\\\\=
6(y+8)(y-5)
.\end{array}
