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The problem asks you to find the quotient:

\[
\frac{-25w^4 - 15w^2}{-5w}
\]

### Step-by-Step Solution:
1. **Factor out the common term from the numerator**:
   The numerator is \( -25w^4 - 15w^2 \), and we can factor out \( -5w^2 \):
   \[
   -5w^2(5w^2 + 3)
   \]

2. **Rewrite the expression**:
   The original expression becomes:
   \[
   \frac{-5w^2(5w^2 + 3)}{-5w}
   \]

3. **Simplify**:
   Cancel the common factor of \( -5w \) from both the numerator and denominator:
   \[
   \frac{-5w^2}{-5w} = w
   \]
   So the expression simplifies to:
   \[
   w(5w + 3)
   \]

### Final Answer:
\[
5w^3 + 3w
\]

Would you like more details on any part of the process?

### Related Questions:
1. How do you factor common terms from an expression?
2. What happens when you divide terms with the same base and different exponents?
3. Can you simplify an expression further if it has no common terms left?
4. How do you check if your simplified expression is correct?
5. Why is it important to cancel common factors in fractions?

**Tip:** Always look for the greatest common factor (GCF) in both the numerator and the denominator to simplify expressions quickly.

Find the quotient: (-25w^4 - 15w^2) / (-5w)

Learn how to simplify the polynomial expression (-25w^4 - 15w^2) divided by (-5w) step by step. This solution focuses on factoring, canceling common terms, and applying exponent laws. Suitable for students in Grades 9-11.

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