Answer
$-(x-1)(x-12)$
Work Step by Step
The given expression, $
-x^2+13x-12
,$ is equivalent to
\begin{align*}
-(x^2-13x+12)
\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{align*}
-(x^2-13x+12)
\end{align*} has $c=
12
$ and $b=
-13
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-1,-12
\right\}.$ Using these two numbers, the factored form of the $\text{
expression
}$ above is
\begin{align*}
&
-(x-1)(x-12)
\end{align*}