https://file.aiquickdraw.com/mathbot/file/1727052838181wa5qmu65.jpg

The polynomial given in the image is:

\[
2a^5b^2 - 7a^3b^3 + 5ab + 7
\]

To determine the degree of a polynomial, you need to find the term with the highest total degree, where the total degree is the sum of the exponents of all variables in each term.

### Let's calculate the degree of each term:

1. **First term**: \(2a^5b^2\)
   - The degree of \(a^5\) is 5.
   - The degree of \(b^2\) is 2.
   - Total degree = \(5 + 2 = 7\).

2. **Second term**: \(-7a^3b^3\)
   - The degree of \(a^3\) is 3.
   - The degree of \(b^3\) is 3.
   - Total degree = \(3 + 3 = 6\).

3. **Third term**: \(5ab\)
   - The degree of \(a\) is 1.
   - The degree of \(b\) is 1.
   - Total degree = \(1 + 1 = 2\).

4. **Fourth term**: \(7\) (a constant)
   - The degree of a constant term is 0.

### Conclusion:
The highest degree among the terms is 7. Therefore, **the degree of the polynomial is 7**.

The correct answer is **A. 7**.

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Would you like more details or have any questions?

Here are 5 related questions you might be interested in:

1. How do you determine the degree of a multivariable polynomial?
2. What is the difference between the degree of a term and the degree of a polynomial?
3. Can a polynomial have negative degrees? Why or why not?
4. How does the degree of a polynomial relate to its graph's behavior?
5. What are some real-world applications of polynomials with degrees higher than 3?

**Tip:** The degree of a polynomial provides insights into the behavior of its graph, particularly the number of possible roots and the end behavior of the function.

Determine the degree of the polynomial 2a^5b^2 - 7a^3b^3 + 5ab + 7.

Learn how to determine the degree of the polynomial 2a^5b^2 - 7a^3b^3 + 5ab + 7. This problem includes calculating the total degree of each term and finding the highest degree term in a multivariable polynomial. Suitable for Grades 9-11.

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