1. **State the problem:** Given $h(x) = f(x)g(x)$, with $f(x) = 2x + 5$ and $h(x) = -2x^2 - 5x$, find $g(x)$. 2. **Formula used:** Since $h(x) = f(x)g(x)$, we can find $g(x)$ by dividing $h(x)$ by $f(x)$: $$g(x) = \frac{h(x)}{f(x)}$$ 3. **Substitute the given functions:** $$g(x) = \frac{-2x^2 - 5x}{2x + 5}$$ 4. **Simplify the expression:** Factor the numerator if possible. $$-2x^2 - 5x = -x(2x + 5)$$ 5. **Rewrite $g(x)$ using the factorization:** $$g(x) = \frac{-x(2x + 5)}{2x + 5}$$ 6. **Cancel common factors:** Since $2x + 5 \neq 0$, we can cancel it out: $$g(x) = -x$$ 7. **Final answer:** $$\boxed{g(x) = -x}$$ This means the function $g(x)$ is simply $-x$.