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