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The degree of a polynomial is the highest power of the variable \( x \) present in the polynomial expression. The given polynomial is:

\[
x^5 + 1 - 3x^4 + 3x^9 - 2x
\]

Now, let's identify the degrees of each term:

- \( x^5 \) has degree 5.
- \( 1 \) (a constant) has degree 0.
- \( -3x^4 \) has degree 4.
- \( 3x^9 \) has degree 9.
- \( -2x \) has degree 1.

The highest degree among these terms is 9, which comes from \( 3x^9 \).

Therefore, the degree of the polynomial is **9**. The correct answer is **D**.

Would you like any further explanation?

Here are 5 related questions to practice:
1. What is the degree of the polynomial \( 2x^7 - x^3 + 4 \)?
2. How does the degree of a polynomial affect its graph?
3. What is the degree of the sum of \( x^4 + 3x^2 \) and \( x^5 - 2x + 1 \)?
4. Can a polynomial have a degree of 0? What would that look like?
5. What is the degree of the product of \( x^2 \) and \( 3x^5 \)?

**Tip:** The degree of a polynomial is key in determining the end behavior of its graph.

What is the degree of the polynomial x^5 + 1 - 3x^4 + 3x^9 - 2x?

Learn how to determine the degree of the polynomial expression x^5 + 1 - 3x^4 + 3x^9 - 2x by identifying the term with the highest exponent. This problem explores fundamental concepts in polynomials, suitable for high school students in Grades 9-12.

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