Answer
$(x-4)(x-12)$
Work Step by Step
The given expression, $
y^2-16y+48
,$ has $c=
48
$ and $b=
-16
.$
The possible factors of $c$ are $
\{ 1,48 \}
,\{ 2,24 \}
,\{ 3,16 \}
,\{ 4,12 \}
,\{ 6,8 \}
,\{ -1,-48 \}
,\{ -2,-24 \}
,\{ -3,-16 \}
,\{ -4,-12 \}
,\{ -6,-8 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-4,-12
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x-4)(x-12)
.\end{array}