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

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

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

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

Answer :

First, we identify the degree of each term in the polynomial
\[
4x^2 - x + 8x^6 + 3 + 2x^{10}.
\]
Here are the terms with their degrees:

- \(2x^{10}\) has degree 10.
- \(8x^6\) has degree 6.
- \(4x^2\) has degree 2.
- \(-x\) has degree 1.
- \(3\) has degree 0.

Next, we arrange the terms in descending order by their exponents (from the highest degree to the lowest):

1. The term with degree 10: \(2x^{10}\)
2. The term with degree 6: \(8x^6\)
3. The term with degree 2: \(4x^2\)
4. The term with degree 1: \(-x\)
5. The constant term (degree 0): \(3\)

Thus, the polynomial written in descending order is:
\[
2x^{10} + 8x^6 + 4x^2 - x + 3.
\]

Comparing with the provided multiple-choice options, the correct answer is:

D. \(2 x^{10}+8 x^6+4 x^2-x+3\).

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