High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which of the following shows the polynomial below written in descending order?

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

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

Answer :

To write the polynomial in descending order, you need to arrange the terms from the highest degree to the lowest degree. The polynomial provided is:

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

Let's identify the terms and their degrees:

1. [tex]\( 3x^{11} \)[/tex] - This term has a degree of 11.
2. [tex]\( 9x^7 \)[/tex] - This term has a degree of 7.
3. [tex]\( 5x^3 \)[/tex] - This term has a degree of 3.
4. [tex]\(-x\)[/tex] - This term can be considered as [tex]\(-1x^1\)[/tex], which has a degree of 1.
5. [tex]\(4\)[/tex] - This is a constant term, with a degree of 0.

Now, we arrange these terms from highest to lowest power:

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

When these terms are arranged in descending order, the polynomial looks like this:

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

Therefore, the correct choice which shows the polynomial written in descending order is option C.