Solution
= Solution
Find two numbers with sum $-1$ and product $-2$: they are $-2$ and $1$. Thus the <quadratic polynomial> factorizes as
$$
\boxed{x^2-x-2=(x-2)(x+1).}
$$
The product is negative precisely when its two factors have opposite signs. This occurs between its two <polynomial roots>, so
$$
\boxed{-1<x<2.}
$$
The endpoints give zero and are excluded by the strict inequality.