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 [tex]$4x^2 - x + 8x^6 + 3 + 2x^{10}$[/tex] in descending order, we need to arrange the terms by the exponent of [tex]$x$[/tex], starting with the highest.

Here's how you can do it step by step:

1. Identify the exponent of each term:
- [tex]$2x^{10}$[/tex]: exponent is 10
- [tex]$8x^6$[/tex]: exponent is 6
- [tex]$4x^2$[/tex]: exponent is 2
- [tex]$-x$[/tex]: exponent is 1
- [tex]$3$[/tex]: exponent is 0 (since it’s a constant)

2. Arrange the terms in descending order of exponents:
- Start with the term with the highest exponent: [tex]$2x^{10}$[/tex]
- Next is: [tex]$8x^6$[/tex]
- Followed by: [tex]$4x^2$[/tex]
- Then: [tex]$-x$[/tex]
- Finally, the constant term: [tex]$3$[/tex]

3. Write the polynomial in the correct order:
- Combine the terms: [tex]$2x^{10} + 8x^6 + 4x^2 - x + 3$[/tex]

Looking at the options provided:

- A. [tex]$8 x^6 + 4 x^2 + 3 + 2 x^{10} - x$[/tex]
- B. [tex]$2 x^{10} + 4 x^2 - x + 3 + 8 x^6$[/tex]
- C. [tex]$3 + 2 x^{10} + 8 x^6 + 4 x^2 - x$[/tex]
- D. [tex]$2 x^{10} + 8 x^6 + 4 x^2 - x + 3$[/tex]

The correct arrangement, [tex]$2x^{10} + 8x^6 + 4x^2 - x + 3$[/tex], matches option D.

Therefore, the correct choice is D.