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

[tex]3x^3 + 9x^7 - x + 4x^{12}[/tex]

A. [tex]9x^7 + 4x^{12} + 3x^3 - x[/tex]

B. [tex]4x^{12} + 9x^7 + 3x^3 - x[/tex]

C. [tex]3x^3 + 4x^{12} + 9x^7 - x[/tex]

D. [tex]4x^{12} + 3x^3 - x + 9x^7[/tex]

Let's arrange the terms of the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order based on the exponents of [tex]\(x\)[/tex]. Here’s how you can do it step by step:

1. Identify the terms:
- [tex]\(4x^{12}\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(3x^3\)[/tex]
- [tex]\(-x\)[/tex] (This is equivalent to [tex]\(-1x^1\)[/tex])

2. Order the terms: Arrange these terms from the highest exponent to the lowest exponent.

3. Highest exponent first:
- The term [tex]\(4x^{12}\)[/tex] has the highest exponent, so it comes first.

4. Next highest exponent:
- The next highest exponent is [tex]\(7\)[/tex], corresponding to the term [tex]\(9x^7\)[/tex].

5. Next is [tex]\(3\)[/tex]:
- The exponent [tex]\(3\)[/tex] comes after that with the term [tex]\(3x^3\)[/tex].

6. Lowest exponent:
- Finally, we have the term [tex]\(-x\)[/tex], which has an exponent of [tex]\(1\)[/tex].

Now, putting all these terms together in descending order, we get:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]

Therefore, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].

Among the choices provided:
- Option B: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex] is the correct arrangement.

The correct answer is B.