#### Answer

$y^2(y-2)(3y+5)$

#### Work Step by Step

Factoring the $GCF=y^2$ of the given expression, $
3y^4-y^3-10y^2
$, results to
\begin{array}{l}\require{cancel}
y^2(3y^2-y-10)
.\end{array}
The two numbers whose product is $ac=
3(-10)=-30
$ and whose sum is $b=
-1
$ are $\{
-6,5
\}$. Using these two numbers to decompose the middle term, then the factored form of the resulting expression, $
y^2(3y^2-y-10)
$,is
\begin{array}{l}\require{cancel}
y^2(3y^2-6y+5y-10)
\\\\=
y^2[(3y^2-6y)+(5y-10)]
\\\\=
y^2[3y(y-2)+5(y-2)]
\\\\=
y^2[(y-2)(3y+5)]
\\\\=
y^2(y-2)(3y+5)
.\end{array}