Answer
$(x-7)(x-1)$
Work Step by Step
The two numbers whose product is $ac=
1(-8)=-8
$ and whose sum is $b=
-2
$ are $\{
-4,2
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
(x-3)^2-2(x-3)-8
$, is
\begin{array}{l}\require{cancel}
(x-3)^2-4(x-3)+2(x-3)-8
\\\\=
[(x-3)^2-4(x-3)]+[2(x-3)-8]
\\\\=
(x-3)[(x-3)-4]+2[(x-3)-4]
\\\\=
[(x-3)-4][(x-3)+2]
\\\\=
[x-3-4][x-3+2]
\\\\=
(x-7)(x-1)
.\end{array}
