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

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

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

To write the polynomial in descending order, we need to arrange the terms from highest to lowest degree according to their exponents.

Here’s the given polynomial:

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

Let's identify the terms and their degrees:

1. [tex]$2x^{10}$[/tex] has degree 10.
2. [tex]$8x^6$[/tex] has degree 6.
3. [tex]$4x^2$[/tex] has degree 2.
4. [tex]$-x$[/tex] has degree 1.
5. The constant term [tex]$3$[/tex] has degree 0.

Now, we arrange these terms in descending order of their degrees:

1. [tex]$2x^{10}$[/tex]
2. [tex]$8x^6$[/tex]
3. [tex]$4x^2$[/tex]
4. [tex]$-x$[/tex]
5. [tex]$+3$[/tex]

Putting them together, the polynomial in descending order is:

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

This matches option C:

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

Therefore, the correct choice is C.