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.
[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.
