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

C. [tex]2x^{10} + 4x^2 - x + 3 + 8x^6[/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, you need to arrange the terms based on the powers of [tex]$x$[/tex] from highest to lowest.

1. First, identify the terms and their respective powers:
- [tex]$2x^{10}$[/tex] (highest power is 10)
- [tex]$8x^6$[/tex] (next highest power is 6)
- [tex]$4x^2$[/tex] (next highest power is 2)
- [tex]$-x$[/tex] (next highest power is 1)
- [tex]$3$[/tex] (constant term with power 0)

2. Arrange these terms in descending order of their powers:
- [tex]$2x^{10}$[/tex] (power 10)
- [tex]$8x^6$[/tex] (power 6)
- [tex]$4x^2$[/tex] (power 2)
- [tex]$-x$[/tex] (power 1)
- [tex]$3$[/tex] (constant term)

Combining these, the polynomial in descending order is:
[tex]\[2x^{10} + 8x^6 + 4x^2 - x + 3\][/tex]

Now, let's match this format to the given choices:

A. [tex]$8x^6 + 4x^2 + 3 + 2x^{10} - x$[/tex] (not in correct order)
B. [tex]$3 + 2x^{10} + 8x^6 + 4x^2 - x$[/tex] (not in correct order)
C. [tex]$2x^{10} + 4x^2 - x + 3 + 8x^6$[/tex] (not in correct order)
D. [tex]$2x^{10} + 8x^6 + 4x^2 - x + 3$[/tex] (correct order)

Therefore, the correct answer is:
D. [tex]$2x^{10} + 8x^6 + 4x^2 - x + 3$[/tex]

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

Answer :

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