Answer
$x(2x-1)(3x+1)$
Work Step by Step
Factoring the $GCF=x$, then the given expression, $
6x^3-x^2-x
$, is equivalent to
\begin{array}{l}
x(6x^2-x-1)
.\end{array}
The two numbers whose product is $ac=
6(-1)=-6
$ and whose sum is $b=
-1
$ are $\{
-3,2
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
x(6x^2-x-1)
$, is
\begin{array}{l}\require{cancel}
x(6x^2-3x+2x-1)
\\\\=
x[(6x^2-3x)+(2x-1)]
\\\\=
x[3x(2x-1)+(2x-1)]
\\\\=
x[(2x-1)(3x+1)]
\\\\=
x(2x-1)(3x+1)
.\end{array}
