Answer
$(x-2y)(x-7y)$
Work Step by Step
The given expression, $
x^2-9xy+14y^2
,$ has $c=
14
$ and $b=
-9
.$
The possible factors of $c$ are $
\{ 1,14 \}
,\{ 2,7 \}
,\{ -1,-14 \}
,\{ -2,-7 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-2,-7
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x-2y)(x-7y)
.\end{array}