Answer
$(x-6)^2$
Work Step by Step
The two numbers whose product is $
36
$ and whose sum is $
-12
$ are $\{
-6,-6\}
$. Using these numbers to decompose the middle term of the trinomial, then,
\begin{array}{l}
x^2-12x+36
\\=
x^2-6x-6x+36
\\=
(x^2-6x)-(6x-36)
\\=
x(x-6)-6(x-6)
\\=
(x-6)(x-6)
\\=
(x-6)^2
.\end{array}
