1. **State the problem:** Simplify the function $f(x) = \frac{x^5 - 2x^3 - 8x^2}{x}$. 2. **Recall the rule:** When dividing a polynomial by $x$, divide each term in the numerator by $x$ separately. 3. **Divide each term:** $$f(x) = \frac{x^5}{x} - \frac{2x^3}{x} - \frac{8x^2}{x}$$ 4. **Simplify each term:** $$f(x) = x^{5-1} - 2x^{3-1} - 8x^{2-1} = x^4 - 2x^2 - 8x$$ 5. **Final simplified function:** $$f(x) = x^4 - 2x^2 - 8x$$ This is the simplified form of the given function after dividing each term by $x$.