Answer
$(x+2)(x-7)$
Work Step by Step
The two numbers whose product is $ac=
1(-18)=-18
$ and whose sum is $b=
3
$ are $\{
6,-3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
(x-4)^2+3(x-4)-18
$, is
\begin{array}{l}\require{cancel}
(x-4)^2+6(x-4)-3(x-4)-18
\\\\=
[(x-4)^2+6(x-4)]-[3(x-4)+18]
\\\\=
(x-4)[(x-4)+6]-3[(x-4)+6]
\\\\=
[(x-4)+6][(x-4)-3]
\\\\=
[x-4+6][x-4-3]
\\\\=
(x+2)(x-7)
.\end{array}
