Answer
$(x-11)(x+9)$
Work Step by Step
In decreasing order of exponents, the given expression, $
-2x-99+x^2
,$ is equivalent to
\begin{array}{l}
x^2-2x-99
.\end{array}
The 2 numbers whose product is $ac=
1(-99)=-99
$ and whose sum is $b=
-2
$ are $\left\{
-11,9
\right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then
\begin{array}{l}
x^2-11x+9x-99
\\\\=
(x^2-11x)+(9x-99)
\\\\=
x(x-11)+9(x-11)
\\\\=
(x-11)(x+9)
.\end{array}
