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To find the degree of the given polynomial, let's analyze each term.

The given polynomial is:

\[
-4u + 15w^9 u^7 v^4 - v^8 w^9 - 6
\]

1. **Identify the degree of each term**:
   - **First term:** \( -4u \) — The degree of \( u \) is 1.
   - **Second term:** \( 15w^9 u^7 v^4 \) — The degree is the sum of the powers of \( w \), \( u \), and \( v \), which is \( 9 + 7 + 4 = 20 \).
   - **Third term:** \( -v^8 w^9 \) — The degree is the sum of the powers of \( v \) and \( w \), which is \( 8 + 9 = 17 \).
   - **Fourth term:** \( -6 \) — This is a constant term, so its degree is 0.

2. **Find the highest degree term**:
   The second term, \( 15w^9 u^7 v^4 \), has the highest degree, which is 20.

Thus, the degree of the polynomial is **20**.

Would you like more details on how I broke down the polynomial, or do you have any other questions?

Here are 5 related questions to expand on this:
1. How do you determine the degree of a polynomial with multiple variables?
2. What is the degree of a monomial like \( x^3 y^2 z^5 \)?
3. How does the degree of a polynomial affect its graph?
4. Can a polynomial have negative exponents, and how would that affect its degree?
5. What is the difference between the degree of a term and the degree of a polynomial?

**Tip:** The degree of a polynomial is the highest sum of the exponents of variables in any single term.

Give the degree of the polynomial -4u + 15w^9 u^7 v^4 - v^8 w^9 - 6.

Learn how to determine the degree of a polynomial with multiple variables. This problem includes terms like -4u, 15w^9 u^7 v^4, and more. The highest degree is calculated by summing the exponents of the variables. Suitable for high school students studying algebra.

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