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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 :

To write the polynomial in descending order, you need to arrange the terms based on the exponents of [tex]\( x \)[/tex] from highest to lowest.

The given polynomial is:

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

Let's organize the terms by the exponents of [tex]\( x \)[/tex]:

1. Identify the term with the highest exponent: [tex]\( 3x^{11} \)[/tex].
2. Next, find the term with the next highest exponent: [tex]\( 9x^7 \)[/tex].
3. Then, the term with the next highest exponent: [tex]\( 5x^3 \)[/tex].
4. The term with [tex]\( x^1 \)[/tex]: [tex]\(-x\)[/tex].
5. Finally, the constant term: [tex]\( 4 \)[/tex].

Arrange these in descending order of their exponents:

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

The polynomial in descending order is:

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

Therefore, the correct choice is:
D. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]

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