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

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

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

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

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

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

To arrange a polynomial in descending order, we need to order all the terms from the highest to the lowest exponent of [tex]$ x $[/tex]. Let's look at the polynomial given:

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

Here are the steps to ordering it:

1. Identify the exponents of each term:
- [tex]$ 3x^{11} $[/tex] has the highest exponent, which is 11.
- [tex]$ 9x^7 $[/tex] has an exponent of 7.
- [tex]$ 5x^3 $[/tex] has an exponent of 3.
- [tex]$ -x $[/tex] can be rewritten as [tex]$-1x^1$[/tex] and has an exponent of 1.
- The constant term [tex]$ 4 $[/tex] can be considered as [tex]$ 4x^0 $[/tex] with an exponent of 0.

2. Reorder the terms from highest to lowest exponent:
- Start with the term with the highest exponent: [tex]$ 3x^{11} $[/tex].
- Next is the term with the next highest exponent: [tex]$ 9x^7 $[/tex].
- Followed by: [tex]$ 5x^3 $[/tex].
- Then: [tex]$-x$[/tex].
- Finally, the constant term: [tex]$ 4 $[/tex].

3. Write the polynomial in descending order:
- Combine all these ordered terms to get:

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

Thus, the polynomial written in descending order is:

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

So, the correct answer is option B:

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