Answer :
To rearrange a polynomial in descending order, you need to order the terms by the degree of [tex]\( x \)[/tex], from the highest power to the lowest. Let’s break this down with the given polynomial:
The polynomial is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Step-by-step solution:
1. Identify the degrees of each term:
- [tex]\( 3x^{11} \)[/tex] has a degree of 11.
- [tex]\( 9x^7 \)[/tex] has a degree of 7.
- [tex]\( 5x^3 \)[/tex] has a degree of 3.
- [tex]\( -x \)[/tex] (which is [tex]\( -1x^1 \)[/tex]) has a degree of 1.
- [tex]\( 4 \)[/tex] (which is [tex]\( 4x^0 \)[/tex]) has a degree of 0.
2. Order the terms from the highest degree to the lowest degree:
When ordering by the degree, the polynomial should be rewritten starting with the term with the highest power:
- Start with [tex]\( 3x^{11} \)[/tex] (degree 11)
- Next is [tex]\( 9x^7 \)[/tex] (degree 7)
- Then [tex]\( 5x^3 \)[/tex] (degree 3)
- Followed by [tex]\( -x \)[/tex] (degree 1)
- Finally, [tex]\( +4 \)[/tex] (degree 0)
3. Write the polynomial in descending order:
Rewriting the polynomial accordingly, we get:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
This matches option A. Therefore, the polynomial in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
So the correct answer is:
A. [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
The polynomial is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Step-by-step solution:
1. Identify the degrees of each term:
- [tex]\( 3x^{11} \)[/tex] has a degree of 11.
- [tex]\( 9x^7 \)[/tex] has a degree of 7.
- [tex]\( 5x^3 \)[/tex] has a degree of 3.
- [tex]\( -x \)[/tex] (which is [tex]\( -1x^1 \)[/tex]) has a degree of 1.
- [tex]\( 4 \)[/tex] (which is [tex]\( 4x^0 \)[/tex]) has a degree of 0.
2. Order the terms from the highest degree to the lowest degree:
When ordering by the degree, the polynomial should be rewritten starting with the term with the highest power:
- Start with [tex]\( 3x^{11} \)[/tex] (degree 11)
- Next is [tex]\( 9x^7 \)[/tex] (degree 7)
- Then [tex]\( 5x^3 \)[/tex] (degree 3)
- Followed by [tex]\( -x \)[/tex] (degree 1)
- Finally, [tex]\( +4 \)[/tex] (degree 0)
3. Write the polynomial in descending order:
Rewriting the polynomial accordingly, we get:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
This matches option A. Therefore, the polynomial in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
So the correct answer is:
A. [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
