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Which of the following shows the polynomial below written in descending order?

[tex]5x^3 - x + 9x^7 + 4 + 3x^{11}[/tex]

A. [tex]4 + 3x^{11} + 9x^7 + 5x^3 - x[/tex]

B. [tex]3x^{11} + 9x^7 - x + 4 + 5x^3[/tex]

C. [tex]9x^7 + 5x^3 + 4 + 3x^{11} - x[/tex]

D. [tex]3x^{11} + 9x^7 + 5x^3 - x + 4[/tex]

Answer :

The original polynomial given is
[tex]$$
5x^3 - x + 9x^7 + 4 + 3x^{11}.
$$[/tex]

We first identify the terms along with their exponents:
- [tex]$5x^3$[/tex] has exponent 3.
- [tex]$-x$[/tex] has exponent 1.
- [tex]$9x^7$[/tex] has exponent 7.
- [tex]$4$[/tex] has exponent 0.
- [tex]$3x^{11}$[/tex] has exponent 11.

To write the polynomial in descending order, we arrange the terms from the highest exponent to the lowest exponent. The exponents in descending order are: 11, 7, 3, 1, and 0.

So, the rearranged polynomial becomes:
[tex]$$
3x^{11} + 9x^7 + 5x^3 - x + 4.
$$[/tex]

Among the options given, this corresponds to option D.

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