Answer
$3x(x+3)(3x-5)$
Work Step by Step
Factoring the $GCF=
3x
$, then the given expression, $
9x^3+12x^2-45x
$ is equivalent to
\begin{array}{l}
3x(3x^2+4x-15)
.\end{array}
The two numbers whose product is $ac=
3(-15)=-45
$ and whose sum is $b=
4
$ are $\{
9,-5
\}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is
\begin{array}{l}
3x(3x^2+4x-15)
\\\\=
3x(3x^2+9x-5x-15)
\\\\=
3x[(3x^2+9x)-(5x+15)]
\\\\=
3x[3x(x+3)-5(x+3)]
\\\\=
3x[(x+3)(3x-5)]
\\\\=
3x(x+3)(3x-5)
.\end{array}
