Answer
$-(x+3)^2$
Work Step by Step
Factoring the $-1,$ the given expression, $
-x^2-6x-9
,$ is equivalent to
\begin{align*}\require{cancel}
&
-(x^2+6x+9)
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the trinomial expression above has $c=
9
$ and $b=
6
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
3,3
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
&
-(x+3)(x+3)
\\&=
-(x+3)^2
.\end{align*}
Hence, the factored form of the given expression is $
-(x+3)^2
$.
