Answer
$24x^3(3x-2)(2x-1)$
Work Step by Step
Factoring the $GCF=
12x^3
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
144x^5-168x^4+48x^3
\\\\=
24x^3(6x^2-7x+2)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
24x^3(6x^2-7x+2)
\end{array} has $ac=
6(2)=12
$ and $b=
-7
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,-3
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
24x^3(6x^2-4x-3x+2)
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
24x^3[(6x^2-4x)-(3x-2)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
24x^3[2x(3x-2)-(3x-2)]
.\end{array}
Factoring the $GCF=
(7x+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
24x^3[(3x-2)(2x-1)]
\\\\=
24x^3(3x-2)(2x-1)
.\end{array}