Answer
$3x(x-25)(x+4)$
Work Step by Step
Factoring the $GCF=
3x
$, the given expression, $
3x^3-63x^2-300x
,$ is equivalent to
\begin{array}{l}
3x(x^2-21x-100)
.\end{array}
The 2 numbers whose product is $ac=
1(-100)=-100
$ and whose sum is $b=
-21
$ are $\left\{
-25,4
\right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then
\begin{array}{l}
3x(x^2-25x+4x-100)
\\\\=
3x[(x^2-25x)+(4x-100)]
\\\\=
3x[x(x-25)+4(x-25)]
\\\\=
3x[(x-25)(x+4)]
\\\\=
3x(x-25)(x+4)
.\end{array}