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------------------------------------------------ Which of the following shows the polynomial below written in descending order?

[tex]3x^3 - 5x + x^7 + 9 + 4x^{11}[/tex]

A. [tex]4x^{11} + x^7 - 5x + 9 + 3x^3[/tex]

B. [tex]x^7 + 3x^3 + 9 + 4x^{11} - 5x[/tex]

C. [tex]4x^{11} + x^7 + 3x^3 - 5x + 9[/tex]

D. [tex]9 + 4x^{11} + x^7 + 3x^3 - 5x[/tex]

We start with the polynomial

$$3x^3 - 5x + x^7 + 9 + 4x^{11}.$$

**Step 1: Identify the terms and their exponents.**
The polynomial has the following terms:
- $3x^3$ (exponent 3)
- $-5x$ (exponent 1)
- $x^7$ (exponent 7)
- $9$ (exponent 0)
- $4x^{11}$ (exponent 11)

**Step 2: Rearrange the terms in descending order (from highest exponent to lowest).**
- The term with the highest exponent is $4x^{11}$ (exponent 11).
- Next comes $x^7$ (exponent 7).
- Then $3x^3$ (exponent 3).
- Followed by $-5x$ (exponent 1).
- Finally, the constant $9$ (exponent 0).

So, the polynomial in descending order is:

$$4x^{11} + x^7 + 3x^3 - 5x + 9.$$

**Step 3: Match with the given choices.**
This corresponds to option C.