1. **State the problem:** Divide the expression $$-3u^2 - 8u$$ by $$u$$ and express the result including any remainder as a simplified fraction. 2. **Write the division:** $$\frac{-3u^2 - 8u}{u}$$ 3. **Split the fraction:** $$\frac{-3u^2}{u} + \frac{-8u}{u}$$ 4. **Simplify each term:** - For $$\frac{-3u^2}{u}$$, cancel one $$u$$: $$\frac{-3\cancel{u}u}{\cancel{u}} = -3u$$ - For $$\frac{-8u}{u}$$, cancel $$u$$: $$\frac{-8\cancel{u}}{\cancel{u}} = -8$$ 5. **Combine the simplified terms:** $$-3u - 8$$ 6. **Conclusion:** The division $$\frac{-3u^2 - 8u}{u}$$ simplifies exactly to $$-3u - 8$$ with no remainder. **Final answer:** $$-3u - 8$$