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

[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]

A. [tex]\[ 8x^6 + 4x^2 + 3 + 2x^{10} - x \][/tex]

B. [tex]\[ 2x^{10} + 4x^2 - x + 3 + 8x^6 \][/tex]

C. [tex]\[ 3 + 2x^{10} + 8x^6 + 4x^2 - x \][/tex]

D. [tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]

To write the polynomial in descending order of its terms based on the powers of [tex]$ x $[/tex], you need to follow these steps:

1. Identify the Terms and their Powers: The polynomial given is [tex]$ 4x^2 - x + 8x^6 + 3 + 2x^{10} $[/tex]. Here are the terms with their powers:
- [tex]$ 2x^{10} $[/tex] with power 10
- [tex]$ 8x^6 $[/tex] with power 6
- [tex]$ 4x^2 $[/tex] with power 2
- [tex]$-x$[/tex] which is the same as [tex]$-1x^1$[/tex], so power 1
- [tex]$ 3 $[/tex] which can be considered as [tex]$ 3x^0 $[/tex], so power 0

2. Order the Terms: Arrange the terms from the highest to the lowest power:
- First, [tex]$ 2x^{10} $[/tex]
- Then, [tex]$ 8x^6 $[/tex]
- Next, [tex]$ 4x^2 $[/tex]
- Followed by, [tex]$-x$[/tex]
- Lastly, [tex]$ 3 $[/tex]

3. Write the Polynomial: Based on the order determined in the previous step, the polynomial becomes:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]

4. Match with Choices: Compare this ordered polynomial with the given choices:
- D: [tex]$ 2x^{10} + 8x^6 + 4x^2 - x + 3 $[/tex]

So, the correct answer is option D.