https://file.aiquickdraw.com/mathbot/file/1725478929899tyv3mr37.jpg

The image shows the problem: "Divide the following polynomial by \( 7a \):"

\[
56a^8 - 28a^6 + 14a^5
\]

### Solution:

To divide each term of the polynomial by \( 7a \), follow these steps:

1. **First Term:**
   \[
   \frac{56a^8}{7a} = \frac{56}{7} \cdot \frac{a^8}{a} = 8a^{8-1} = 8a^7
   \]

2. **Second Term:**
   \[
   \frac{28a^6}{7a} = \frac{28}{7} \cdot \frac{a^6}{a} = 4a^{6-1} = 4a^5
   \]

3. **Third Term:**
   \[
   \frac{14a^5}{7a} = \frac{14}{7} \cdot \frac{a^5}{a} = 2a^{5-1} = 2a^4
   \]

### Final Answer:
After dividing each term by \( 7a \), the resulting polynomial is:

\[
8a^7 - 4a^5 + 2a^4
\]

Would you like more details or have any questions?

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### Related Questions:
1. How do you divide polynomials by monomials with multiple variables?
2. Can you explain the distributive property used in polynomial division?
3. What happens if the polynomial degree is lower than the monomial divisor's degree?
4. How would you handle division by a polynomial instead of a monomial?
5. What are some common mistakes to avoid when dividing polynomials?

### Tip:
Always check the degree of each term in both the polynomial and the divisor to ensure you simplify the division correctly.

Divide the following polynomial by 7a: 56a^8 - 28a^6 + 14a^5

This page explains how to divide the polynomial 56a^8 - 28a^6 + 14a^5 by 7a, covering key algebraic concepts like polynomial division and simplifying monomials. Suitable for students in Grades 9-10.

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