Answer
$(x+3)^2$
Work Step by Step
The two numbers whose product is $ac=
1(9)=9
$ and whose sum is $b=
6
$ are $\{
3,3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
x^2+6x+9
$, is
\begin{array}{l}\require{cancel}
x^2+3x+3x+9
\\\\=
(x^2+3x)+(3x+9)
\\\\=
x(x+3)+3(x+3)
\\\\=
(x+3)(x+3)
\\\\=
(x+3)^2
.\end{array}
