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The problem asks to divide the polynomial \( 5a^3b - 6a^2b^2 + 4ab^3 \) by \( 5a \).

Let's go through the division step by step:

1. **Divide each term of the polynomial by \( 5a \)**:
   - First term: \( \frac{5a^3b}{5a} = a^2b \)
   - Second term: \( \frac{6a^2b^2}{5a} = \frac{6}{5}ab^2 \)
   - Third term: \( \frac{4ab^3}{5a} = \frac{4}{5}b^3 \)

2. **Combine the results**:
   - The resulting polynomial after dividing by \( 5a \) is:
     \[
     a^2b - \frac{6}{5}ab^2 + \frac{4}{5}b^3
     \]

So, the answer is \( a^2b - \frac{6}{5}ab^2 + \frac{4}{5}b^3 \).

Would you like more details or have any questions about this process? Here are some related questions you might find interesting:

1. How do you divide polynomials by monomials in general?
2. What happens when you divide a polynomial by a binomial?
3. How can you check your answer after dividing polynomials?
4. What are some common mistakes to avoid when dividing polynomials?
5. How would the problem change if you divided by a different term, like \( a^2 \)?

**Tip:** When dividing polynomials by monomials, remember to apply the division to each term separately for accuracy.

Divide the following polynomial: 5a^3b - 6a^2b^2 + 4ab^3 by 5a.

Learn how to divide the polynomial 5a^3b - 6a^2b^2 + 4ab^3 by 5a with this step-by-step guide. This problem covers key algebra concepts, including polynomial division and laws of exponents. Suitable for students in Grades 8-10.

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