Answer :
To write the polynomial in descending order, we need to organize the terms by the exponents of [tex]\( x \)[/tex], starting with the highest power and working down to the lowest. Let's look at the polynomial given:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Here are the steps to rearrange it in descending order:
1. Identify the powers of [tex]\( x \)[/tex] in each term:
- [tex]\( 3x^{11} \)[/tex] has the highest power, which is 11.
- [tex]\( 9x^7 \)[/tex] has the next highest power, which is 7.
- [tex]\( 5x^3 \)[/tex] follows with power 3.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex] with power 1.
- [tex]\(4\)[/tex] is a constant term or [tex]\(4x^0\)[/tex].
2. Order the terms from highest to lowest power:
- Start with [tex]\( 3x^{11} \)[/tex] because it has the highest power.
- Next, take [tex]\( 9x^7 \)[/tex].
- Then use [tex]\( 5x^3 \)[/tex].
- Follow it with [tex]\(-x\)[/tex].
- Finally, add the constant [tex]\( 4 \)[/tex].
So, the polynomial written in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
From the provided options, this corresponds to choice:
C. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Here are the steps to rearrange it in descending order:
1. Identify the powers of [tex]\( x \)[/tex] in each term:
- [tex]\( 3x^{11} \)[/tex] has the highest power, which is 11.
- [tex]\( 9x^7 \)[/tex] has the next highest power, which is 7.
- [tex]\( 5x^3 \)[/tex] follows with power 3.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex] with power 1.
- [tex]\(4\)[/tex] is a constant term or [tex]\(4x^0\)[/tex].
2. Order the terms from highest to lowest power:
- Start with [tex]\( 3x^{11} \)[/tex] because it has the highest power.
- Next, take [tex]\( 9x^7 \)[/tex].
- Then use [tex]\( 5x^3 \)[/tex].
- Follow it with [tex]\(-x\)[/tex].
- Finally, add the constant [tex]\( 4 \)[/tex].
So, the polynomial written in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
From the provided options, this corresponds to choice:
C. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
