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

Answer :

To write the polynomial in descending order, we need to arrange the terms from the highest degree (exponent) to the lowest degree. Let's look at the polynomial given:

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

Here's how you can arrange it:

1. Identify the degrees (exponents) of each term:
- [tex]\(2x^{10}\)[/tex]: The degree is 10.
- [tex]\(8x^6\)[/tex]: The degree is 6.
- [tex]\(4x^2\)[/tex]: The degree is 2.
- [tex]\(-x\)[/tex]: The degree is 1.
- [tex]\(3\)[/tex]: This is a constant term with a degree of 0.

2. Order the terms from highest to lowest degree:
- Start with the term with the highest degree: [tex]\(2x^{10}\)[/tex].
- Next is the term with degree 6: [tex]\(8x^6\)[/tex].
- Then the term with degree 2: [tex]\(4x^2\)[/tex].
- After that, the term with degree 1: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\(3\)[/tex].

Putting it all together, the polynomial written in descending order is:

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

This matches the first option provided in the multiple choice answers:

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

Therefore, this is the correct choice.

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