1. **State the problem:** Divide the polynomial $56m^3 - 32m^2 + 8m$ by $8m$ and express the remainder as a simplified fraction if any. 2. **Write the division expression:** $$\frac{56m^3 - 32m^2 + 8m}{8m}$$ 3. **Divide each term separately:** $$\frac{56m^3}{8m} - \frac{32m^2}{8m} + \frac{8m}{8m}$$ 4. **Simplify each term:** - For $\frac{56m^3}{8m}$, divide coefficients and subtract exponents: $$\frac{56}{8} m^{3-1} = 7m^2$$ - For $\frac{32m^2}{8m}$: $$\frac{32}{8} m^{2-1} = 4m$$ - For $\frac{8m}{8m}$: $$\frac{8}{8} m^{1-1} = 1$$ 5. **Combine the simplified terms:** $$7m^2 - 4m + 1$$ 6. **Check for remainder:** Since the division is exact (no leftover terms), there is no remainder. **Final answer:** $$7m^2 - 4m + 1$$