1. **State the problem:** We need to find the quotient of the polynomial $$-25z^4 - 5z^3$$ divided by the monomial $$-5z^2$$. 2. **Write the division expression:** $$\frac{-25z^4 - 5z^3}{-5z^2}$$ 3. **Use the property of division over addition:** $$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$$ So, $$\frac{-25z^4}{-5z^2} + \frac{-5z^3}{-5z^2}$$ 4. **Simplify each term separately:** - For the first term: $$\frac{-25z^4}{-5z^2} = \frac{\cancel{-25}^5 \cancel{z^4}^{z^2 \cdot z^2}}{\cancel{-5}^1 \cancel{z^2}^{z^2}} = 5z^{4-2} = 5z^2$$ - For the second term: $$\frac{-5z^3}{-5z^2} = \frac{\cancel{-5}^1 \cancel{z^3}^{z^2 \cdot z}}{\cancel{-5}^1 \cancel{z^2}^{z^2}} = 1 \cdot z^{3-2} = z$$ 5. **Combine the simplified terms:** $$5z^2 + z$$ **Final answer:** $$5z^2 + z$$