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

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

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

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

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

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

We are given the polynomial

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

To write it in descending order, we need to arrange the terms based on their exponents, starting with the term with the highest exponent and working down.

1. Look at the exponents of each term:
- The term [tex]$3x^3$[/tex] has exponent 3.
- The term [tex]$9x^7$[/tex] has exponent 7.
- The term [tex]$-x$[/tex] has an implied exponent 1.
- The term [tex]$4x^{12}$[/tex] has exponent 12.

2. Arrange the exponents in descending order: [tex]$12, 7, 3, 1$[/tex].

3. Write the polynomial with the terms in that order:

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

Comparing this with the options provided, it matches option B.

Thus, the answer is option B.