Answer
$y(4y-1)(6y+1)$
Work Step by Step
Factoring the $GCF=y$, then the given expression, $
24y^3-2y^2-y
$, is equivalent to
\begin{array}{l}\require{cancel}
y(24y^2-2y-1)
.\end{array}
The two numbers whose product is $ac=
24(-1)=-24
$ and whose sum is $b=
-2
$ are $\{
-6,4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
y(24y^2-2y-1)
$, is
\begin{array}{l}\require{cancel}
y(24y^2-6y+4y-1)
\\\\=
y[(24y^2-6y)+(4y-1)]
\\\\=
y[6y(4y-1)+(4y-1)]
\\\\=
y[(4y-1)(6y+1)]
\\\\=
y(4y-1)(6y+1)
.\end{array}
