To arrange the given polynomial in descending order, we must organize the terms based on the exponents of [tex]\(x\)[/tex] from highest to lowest. Let's start by examining each term in the original polynomial:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
### Step 1: Identify the Terms and Their Exponents
- [tex]\(3x^{11}\)[/tex]: The exponent of [tex]\(x\)[/tex] is 11.
- [tex]\(9x^7\)[/tex]: The exponent of [tex]\(x\)[/tex] is 7.
- [tex]\(5x^3\)[/tex]: The exponent of [tex]\(x\)[/tex] is 3.
- [tex]\(-x\)[/tex]: The exponent of [tex]\(x\)[/tex] is 1 (since [tex]\(x\)[/tex] is the same as [tex]\(1x^1\)[/tex]).
- [tex]\(4\)[/tex]: The exponent of [tex]\(x\)[/tex] is 0 (since constants can be written as [tex]\(4x^0\)[/tex]).
### Step 2: Arrange Terms by Exponents in Descending Order
Next, we need to write the terms in order from the highest exponent to the lowest:
- First, we have [tex]\(3x^{11}\)[/tex] (highest exponent, 11).
- Then, [tex]\(9x^7\)[/tex] (second highest exponent, 7).
- Followed by [tex]\(5x^3\)[/tex] (third highest exponent, 3).
- Next, [tex]\(-x\)[/tex] (next exponent, 1).
- Finally, [tex]\(4\)[/tex] (constant term with exponent 0).
Putting it all together, the polynomial in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
### Step 3: Match to the Given Choices
Now, we look through the choices provided:
A. [tex]\(3x^{11} + 9x^7 - x + 4 + 5x^3\)[/tex]
B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
C. [tex]\(9x^7 + 5x^3 + 4 + 3x^{11} - x\)[/tex]
### Step 4: Select the Correct Answer
The arrangement we derived matches exactly with choice B:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
Thus, the polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] written in descending order is correctly shown as [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
