Factor the expression by grouping. First, the expression needs to be rewritten as $-x^{2}+ax+bx+2$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-1$$ $$ab=-2=-2$$
Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
$$a=1$$ $$b=-2$$
Rewrite $-x^{2}-x+2$ as $\left(-x^{2}+x\right)+\left(-2x+2\right)$.
$$\left(-x^{2}+x\right)+\left(-2x+2\right)$$
Factor out $x$ in the first and $2$ in the second group.
$$x\left(-x+1\right)+2\left(-x+1\right)$$
Factor out common term $-x+1$ by using distributive property.
