College

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

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

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

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

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

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

Answer :

To write the given polynomial in descending order, we'll arrange the terms by the powers of [tex]\(x\)[/tex], starting from the highest power down to the lowest.

Given polynomial: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]

Let's identify each term by its power of [tex]\(x\)[/tex]:

1. [tex]\(3x^{11}\)[/tex] has the highest power, which is 11.
2. [tex]\(9x^7\)[/tex] is next with power 7.
3. [tex]\(5x^3\)[/tex] follows with power 3.
4. [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex], with power 1.
5. The constant term [tex]\(4\)[/tex] can be thought of as [tex]\(4x^0\)[/tex], with power 0.

We will place these terms in descending order of their powers:

1. [tex]\(3x^{11}\)[/tex]
2. [tex]\(9x^7\)[/tex]
3. [tex]\(5x^3\)[/tex]
4. [tex]\(-x\)[/tex]
5. [tex]\(+4\)[/tex]

Putting them together, we get the polynomial written in descending order:

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

So, the correct expression in descending order is:

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