Answer
$x(4x-1)(3x+1)$
Work Step by Step
Factoring the $GCF=x$, then the given expression, $
12x^3+x^2-x
$, is equivalent to
\begin{array}{l}
x(12x^2+x-1)
.\end{array}
The two numbers whose product is $ac=
12(-1)=-12
$ and whose sum is $b=
1
$ are $\{
-3,4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
x(12x^2+x-1)
$, is
\begin{array}{l}\require{cancel}
x(12x^2-3x+4x-1)
\\\\=
x[(12x^2-3x)+(4x-1)]
\\\\=
x[3x(4x-1)+(4x-1)]
\\\\=
x[(4x-1)(3x+1)]
\\\\=
x(4x-1)(3x+1)
.\end{array}
