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To determine the degree of the given polynomial, we need to find the highest sum of exponents of the variables in any term of the polynomial. Let's examine the polynomial:

\[
6y^8 + 9v^4 y^2 x - 6 + x^4 v^2
\]

Now, we'll look at each term:

1. \( 6y^8 \): The degree is 8 (since the exponent of \( y \) is 8).
2. \( 9v^4 y^2 x \): The degree is \( 4 + 2 + 1 = 7 \) (summing the exponents of \( v \), \( y \), and \( x \)).
3. \( -6 \): This is a constant term, so the degree is 0.
4. \( x^4 v^2 \): The degree is \( 4 + 2 = 6 \) (summing the exponents of \( x \) and \( v \)).

The highest degree among these terms is 8 (from \( 6y^8 \)).

Thus, the degree of the polynomial is **8**.

Would you like further details or explanations on any part of this?

Here are 5 related questions to deepen your understanding:
1. How do you determine the degree of a term with multiple variables?
2. What is the degree of a constant polynomial?
3. Can a polynomial have more than one term with the highest degree?
4. How does the degree of a polynomial affect its graph?
5. What is the difference between the degree of a term and the degree of a polynomial?

**Tip**: The degree of a polynomial gives an idea of the highest power of the variable(s) involved, which also indicates the potential complexity of its graph!

Give the degree of the polynomial: 6y^8 + 9v^4 y^2 x - 6 + x^4 v^2

Learn how to determine the degree of the polynomial 6y^8 + 9v^4 y^2 x - 6 + x^4 v^2 with a step-by-step explanation. This problem covers polynomial degree calculation and is suitable for students in Grades 8-10.

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