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

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

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

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

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

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

To write the polynomial [tex]$2x^2 - 4x + x^6 + 8 + 3x^{10}$[/tex] in descending order, you'll want to list the terms from the highest degree to the lowest degree. Here's how you can do that:

1. Identify the terms and their degrees:
- [tex]$3x^{10}$[/tex]: degree 10
- [tex]$x^6$[/tex]: degree 6
- [tex]$2x^2$[/tex]: degree 2
- [tex]$-4x$[/tex]: degree 1
- [tex]$8$[/tex]: degree 0

2. Reorder the terms by their degrees, from highest to lowest:
- Start with the term with the highest degree: [tex]$3x^{10}$[/tex]
- Next, include the term with the second highest degree: [tex]$x^6$[/tex]
- Then add the term with the next degree: [tex]$2x^2$[/tex]
- Follow with the term of degree 1: [tex]$-4x$[/tex]
- Finally, add the constant term: [tex]$8$[/tex]

3. Put it all together:
- The polynomial in descending order is: [tex]$3x^{10} + x^6 + 2x^2 - 4x + 8$[/tex]

Among the options given, option B matches this order:
B. [tex]$3x^{10} + x^6 + 2x^2 - 4x + 8$[/tex]

Therefore, the correct answer is B.