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The given polynomial is:

\[
-3y^4 + 8y^3 - 8y^2 + y + 7
\]

To determine the degree of the polynomial, we need to find the highest power of the variable \(y\). Here are the powers of \(y\) in the terms:

- \(y^4\)
- \(y^3\)
- \(y^2\)
- \(y^1\) (for \(y\))
- \(y^0\) (for the constant 7)

The highest power of \(y\) is 4, so the degree of the polynomial is 4.

Thus, the correct answer is **D. 4**.

Would you like more details or explanations on this? Here are 5 related questions to expand your understanding:

1. What is the significance of the degree of a polynomial?
2. How do you determine the degree of a polynomial with multiple variables?
3. Can a polynomial have a negative degree?
4. What is the degree of a constant polynomial?
5. How does the degree of a polynomial affect its graph?

**Tip:** The degree of a polynomial tells you the highest power of the variable and often determines the general shape of the polynomial's graph.

Determine the degree of the polynomial: -3y^4 + 8y^3 - 8y^2 + y + 7

Find out how to determine the degree of the polynomial -3y^4 + 8y^3 - 8y^2 + y + 7. This problem focuses on identifying the highest exponent of the variable in a polynomial, suitable for high school students.

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