Answer
$x(x-4)(x-20)$
Work Step by Step
Factoring the $GCF=x,$ the given expression, $
x^3-24x^2+80x
,$ is equivalent to
\begin{align*}
&
x(x^2-24x+80)
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c$ method, the $\text{
expression
}$
\begin{array}{l}\require{cancel}
x^2-24x+80
\end{array} has $c=
80
$ and $b=
-24
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,-20
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
x(x-4)(x-20)
.\end{array}
Hence, the factored form of $x^3-24x^2+80x$ is $
x(x-4)(x-20)
$.
