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

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

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

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

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

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

Answer :

The goal is to rewrite the polynomial in descending order by the degree of each term. Consider the polynomial:

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

Each term has a degree based on its exponent:

- The term [tex]$4x^{11}$[/tex] has degree 11.
- The term [tex]$x^7$[/tex] has degree 7.
- The term [tex]$3x^3$[/tex] has degree 3.
- The term [tex]$-5x$[/tex] has degree 1.
- The constant [tex]$9$[/tex] has degree 0.

Arranging these terms from the highest degree to the lowest, we get:

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

Thus, the polynomial in descending order is:

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

Comparing with the provided options, the correct choice is option B.

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