https://file.aiquickdraw.com/mathbot/file/172591718814090bv197c.jpg

To determine the degree of the expression:

\[
-8x^4 y^5 + 9y^7 - 3xy^4 - 6x - 2
\]

### Steps:
1. **Degree of a term** is the sum of the exponents of the variables in that term.
2. We analyze each term individually:

   - \( -8x^4 y^5 \): The exponents are 4 (for \(x\)) and 5 (for \(y\)). So, the total degree is \(4 + 5 = 9\).
   - \( 9y^7 \): The exponent of \(y\) is 7. There is no \(x\), so the degree is 7.
   - \( -3xy^4 \): The exponents are 1 (for \(x\)) and 4 (for \(y\)). So, the total degree is \(1 + 4 = 5\).
   - \( -6x \): The exponent of \(x\) is 1. There is no \(y\), so the degree is 1.
   - \( -2 \): This is a constant term, so the degree is 0.

3. The degree of the entire expression is the highest degree among all terms. The highest degree is 9 (from \( -8x^4 y^5 \)).

### Conclusion:
The degree of the expression is **9**.

The correct option is \( \text{c} \).

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Would you like more details or have any questions?

Here are some related questions to further explore the concept:
1. How do we find the degree of a polynomial in multiple variables?
2. What is the degree of a polynomial with only one variable?
3. Can a constant have a degree? Why or why not?
4. How do coefficients affect the degree of a polynomial?
5. What is the degree of a product of two polynomials?

**Tip:** When finding the degree of a polynomial, always focus on the term with the highest sum of variable exponents.

What is the degree of the expression: -8x^4 y^5 + 9y^7 - 3xy^4 - 6x - 2?

Learn how to determine the degree of the polynomial expression -8x^4 y^5 + 9y^7 - 3xy^4 - 6x - 2. This problem explores the concept of polynomial degrees and terms. Suitable for students in Grades 9-10.

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