Answer
$y^2(y-5)(y-7)$
Work Step by Step
Factoring the $GCF=
y^2
,$ the given expression, $
y^4-12y^3+35y^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
y^2(y^2-12y+35)
.\end{array}
The trinomial expression above has $c=
35
$ and $b=
-12
.$
The possible factors of $c$ are $
\{ 1,35 \}
,\{ 5,7 \}
,\{ -1,-35 \}
,\{ -5,-7 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-5,-7
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
y^2(y-5)(y-7)
.\end{array}
