Answer :
To write the given polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order, we'll need to arrange the terms from the highest power of [tex]\(x\)[/tex] to the lowest. Let's go through the steps:
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] has a power of 3.
- [tex]\(-x\)[/tex] is actually [tex]\(-1x^1\)[/tex], with a power of 1.
- The term [tex]\(4\)[/tex] is a constant, equivalent to [tex]\(4x^0\)[/tex], with a power of 0.
2. Arrange the terms in descending order based on the power of [tex]\(x\)[/tex]:
- Start with the term that has the highest power, which is [tex]\(3x^{11}\)[/tex].
- Next is the term with the second highest power, [tex]\(9x^7\)[/tex].
- The following term is [tex]\(5x^3\)[/tex].
- Then, the term [tex]\(-x\)[/tex] (written as [tex]\(-1x\)[/tex]) comes next.
- Finally, the constant term [tex]\(4\)[/tex].
3. Write the polynomial in descending order:
- Combining our ordered terms gives us: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
Therefore, the polynomial written in descending order is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]. The correct option that matches this order is option C.
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] has a power of 3.
- [tex]\(-x\)[/tex] is actually [tex]\(-1x^1\)[/tex], with a power of 1.
- The term [tex]\(4\)[/tex] is a constant, equivalent to [tex]\(4x^0\)[/tex], with a power of 0.
2. Arrange the terms in descending order based on the power of [tex]\(x\)[/tex]:
- Start with the term that has the highest power, which is [tex]\(3x^{11}\)[/tex].
- Next is the term with the second highest power, [tex]\(9x^7\)[/tex].
- The following term is [tex]\(5x^3\)[/tex].
- Then, the term [tex]\(-x\)[/tex] (written as [tex]\(-1x\)[/tex]) comes next.
- Finally, the constant term [tex]\(4\)[/tex].
3. Write the polynomial in descending order:
- Combining our ordered terms gives us: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
Therefore, the polynomial written in descending order is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]. The correct option that matches this order is option C.
