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]

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).

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 :

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