Answer :
To determine which option shows the polynomial written in descending order, we need to arrange its terms by the power of [tex]\(x\)[/tex], starting from the highest power to the lowest. Here's the step-by-step process:
1. Identify the terms of the polynomial:
The given polynomial is [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex].
2. List the terms with their powers of [tex]\(x\)[/tex]:
- [tex]\(3x^{11}\)[/tex] (highest power, 11)
- [tex]\(9x^7\)[/tex] (next highest power, 7)
- [tex]\(5x^3\)[/tex] (next power, 3)
- [tex]\(-x\)[/tex] (with power 1)
- [tex]\(4\)[/tex] (constant term, with power 0)
3. Arrange the terms in descending order of the power of [tex]\(x\)[/tex]:
We start with the term with the highest power, [tex]\(x^{11}\)[/tex], and proceed to the lowest power, which is the constant term.
- [tex]\(3x^{11}\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(5x^3\)[/tex]
- [tex]\(-x\)[/tex]
- [tex]\(4\)[/tex]
Thus, the polynomial written in descending order is:
[tex]\[3x^{11} + 9x^7 + 5x^3 - x + 4\][/tex]
4. Match the arranged polynomial with the given options:
- Option A: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
Given the arrangement, Option A is the correct answer because it matches the polynomial in descending order:
Answer: A. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
1. Identify the terms of the polynomial:
The given polynomial is [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex].
2. List the terms with their powers of [tex]\(x\)[/tex]:
- [tex]\(3x^{11}\)[/tex] (highest power, 11)
- [tex]\(9x^7\)[/tex] (next highest power, 7)
- [tex]\(5x^3\)[/tex] (next power, 3)
- [tex]\(-x\)[/tex] (with power 1)
- [tex]\(4\)[/tex] (constant term, with power 0)
3. Arrange the terms in descending order of the power of [tex]\(x\)[/tex]:
We start with the term with the highest power, [tex]\(x^{11}\)[/tex], and proceed to the lowest power, which is the constant term.
- [tex]\(3x^{11}\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(5x^3\)[/tex]
- [tex]\(-x\)[/tex]
- [tex]\(4\)[/tex]
Thus, the polynomial written in descending order is:
[tex]\[3x^{11} + 9x^7 + 5x^3 - x + 4\][/tex]
4. Match the arranged polynomial with the given options:
- Option A: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
Given the arrangement, Option A is the correct answer because it matches the polynomial in descending order:
Answer: A. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
