High School

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

Answer :

To arrange the polynomial [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex] in descending order, you need to organize the terms based on the degree of [tex]\(x\)[/tex], starting from the highest to the lowest.

Here’s how to do it step-by-step:

1. Identify the Degrees of Each Term:
- [tex]\(4x^2\)[/tex] has a degree of 2.
- [tex]\(-x\)[/tex] has a degree of 1.
- [tex]\(8x^6\)[/tex] has a degree of 6.
- [tex]\(3\)[/tex] (the constant term) effectively has a degree of 0.
- [tex]\(2x^{10}\)[/tex] has a degree of 10.

2. Arrange the Terms in Descending Order of Degree:
- Start with the term that has the highest degree: [tex]\(2x^{10}\)[/tex].
- Next is the degree 6 term: [tex]\(8x^6\)[/tex].
- Then, the degree 2 term: [tex]\(4x^2\)[/tex].
- Followed by the degree 1 term: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\(3\)[/tex].

3. Write the Polynomial in Order:
- Combine all these terms while keeping their original coefficients and signs.

The polynomial arranged in descending order is:

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

Therefore, the correct option is:

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

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