Answer
$(x-9)(x-10)$
Work Step by Step
Let $z=
(x-2)
.$ The given expression, $
(x-2)^2-15(x-2)+56
,$ is equivalent to
\begin{align*}
z^2-15z+56
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c=
56
$ and $b=
-15
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-7,-8
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
(z-7)(z-8)
.\end{align*}
Substituting back $z=
(x-2),$ the expression above is equivalent to
\begin{align*}
&
(x-2-7)(x-2-8)
\\&=
(x-9)(x-10)
.\end{align*}