Answer
$3(x+5)(x-3)$
Work Step by Step
Factoring the $GCF=3$, then the given expression, $
3x^2+6x-45
$, is equivalent to
\begin{array}{l}
3(x^2+2x-15)
.\end{array}
The two numbers whose product is $ac=
1(-15)=-15
$ and whose sum is $b=
2
$ are $\{
5,-3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3(x^2+2x-15)
$, is
\begin{array}{l}\require{cancel}
3(x^2+5x-3x-15)
\\\\=
3[(x^2+5x)-(3x+15)]
\\\\=
3[x(x+5)-3(x+5)]
\\\\=
3[(x+5)(x-3)]
\\\\=
3(x+5)(x-3)
.\end{array}
