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} + 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 :

We start with the polynomial

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

To write it in descending order, we need to arrange its terms so that the exponents of [tex]\( x \)[/tex] decrease from left to right.

1. Identify the exponents:
- The term [tex]\(2x^{10}\)[/tex] has exponent [tex]\(10\)[/tex].
- The term [tex]\(8x^6\)[/tex] has exponent [tex]\(6\)[/tex].
- The term [tex]\(4x^2\)[/tex] has exponent [tex]\(2\)[/tex].
- The term [tex]\(-x\)[/tex] has exponent [tex]\(1\)[/tex].
- The constant [tex]\(3\)[/tex] has exponent [tex]\(0\)[/tex].

2. Arrange the terms from highest to lowest exponent:
- First, [tex]\(2x^{10}\)[/tex] (exponent [tex]\(10\)[/tex]).
- Then, [tex]\(8x^6\)[/tex] (exponent [tex]\(6\)[/tex]).
- Next, [tex]\(4x^2\)[/tex] (exponent [tex]\(2\)[/tex]).
- Followed by [tex]\(-x\)[/tex] (exponent [tex]\(1\)[/tex]).
- Finally, [tex]\(3\)[/tex] (exponent [tex]\(0\)[/tex]).

Thus, the polynomial in descending order becomes

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

Comparing with the given options, this matches option D.

Therefore, the correct answer is option D (which corresponds to answer number 4).