Answer
$(x-4)(x-18)$
Work Step by Step
The given expression, $
y^2-22y+72
,$ has $c=
72
$ and $b=
-22
.$
The possible factors of $c$ are $
\{ 1,72 \}
,\{ 2,36 \}
,\{ 3,24 \}
,\{ 4,18 \}
,\{ 6,12 \}
,\{ 8,9 \}
,\{ -1,-72 \}
,\{ -2,-36 \}
,\{ -3,-24 \}
,\{ -4,-18 \}
,\{ -6,-12 \}
,\{ -8,-9 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-4,-18
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x-4)(x-18)
.\end{array}
