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Answer :
To write the given polynomial in descending order, you need to arrange the terms based on the powers of [tex]\( x \)[/tex] from the highest to the lowest. The polynomial given is:
[tex]\( 5x^3 - x + 9x^7 + 4 + 3x^{11} \)[/tex].
Let's follow these steps:
1. Identify the powers of [tex]\( x \)[/tex]: Look at each term and find the exponent. The terms are:
- [tex]\( 5x^3 \)[/tex] (power 3)
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex], power 1)
- [tex]\(9x^7\)[/tex] (power 7)
- [tex]\(4\)[/tex] (which is a constant term, power 0)
- [tex]\(3x^{11}\)[/tex] (power 11).
2. Order the terms by descending power of [tex]\( x \)[/tex]: Start with the highest power and move to the lowest:
- Highest power is [tex]\(3x^{11}\)[/tex].
- Next is [tex]\(9x^7\)[/tex].
- Then [tex]\(5x^3\)[/tex].
- Then [tex]\(-x\)[/tex].
- Finally [tex]\(+4\)[/tex].
3. Write the terms in the correct order: Once the terms are ordered by their powers, the polynomial becomes:
- [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
This reveals that the polynomial written in descending order is:
[tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
Therefore, the correct option is:
C. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
[tex]\( 5x^3 - x + 9x^7 + 4 + 3x^{11} \)[/tex].
Let's follow these steps:
1. Identify the powers of [tex]\( x \)[/tex]: Look at each term and find the exponent. The terms are:
- [tex]\( 5x^3 \)[/tex] (power 3)
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex], power 1)
- [tex]\(9x^7\)[/tex] (power 7)
- [tex]\(4\)[/tex] (which is a constant term, power 0)
- [tex]\(3x^{11}\)[/tex] (power 11).
2. Order the terms by descending power of [tex]\( x \)[/tex]: Start with the highest power and move to the lowest:
- Highest power is [tex]\(3x^{11}\)[/tex].
- Next is [tex]\(9x^7\)[/tex].
- Then [tex]\(5x^3\)[/tex].
- Then [tex]\(-x\)[/tex].
- Finally [tex]\(+4\)[/tex].
3. Write the terms in the correct order: Once the terms are ordered by their powers, the polynomial becomes:
- [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
This reveals that the polynomial written in descending order is:
[tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
Therefore, the correct option is:
C. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
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