#### Answer

$(2x-3)^2$

#### Work Step by Step

The two numbers whose product is $ac=
4(9)=36
$ and whose sum is $b=
-12
$ are $\{
-6,-6
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
4x^2-12x+9
$, is
\begin{array}{l}\require{cancel}
4x^2-6x-6x+9
\\\\=
(4x^2-6x)-(6x-9)
\\\\=
2x(2x-3)-3(2x-3)
\\\\=
(2x-3)(2x-3)
\\\\=
(2x-3)^2
.\end{array}