Answer :
To write the polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order, we'll rearrange the terms from the highest power to the lowest power of [tex]\(x\)[/tex].
Here are the steps to follow:
1. Identify the Powers of [tex]\(x\)[/tex]:
- [tex]\(3x^{11}\)[/tex]: The term with the highest power is [tex]\(x^{11}\)[/tex].
- [tex]\(9x^7\)[/tex]: The next highest power is [tex]\(x^7\)[/tex].
- [tex]\(5x^3\)[/tex]: Then, the power is [tex]\(x^3\)[/tex].
- [tex]\(-x\)[/tex]: The power of [tex]\(x\)[/tex] here is [tex]\(x^1\)[/tex].
- [tex]\(4\)[/tex]: This is a constant term with [tex]\(x^0\)[/tex].
2. Arrange Terms by Exponents:
- Write the terms in order from highest to lowest power of [tex]\(x\)[/tex]: [tex]\(3x^{11}\)[/tex], [tex]\(9x^7\)[/tex], [tex]\(5x^3\)[/tex], [tex]\(-x\)[/tex], and [tex]\(4\)[/tex].
3. Combine the Terms:
- Combine these terms into one polynomial: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
After arranging them correctly, the polynomial in descending order is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
Therefore, the correct option from the given choices is:
- B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
Here are the steps to follow:
1. Identify the Powers of [tex]\(x\)[/tex]:
- [tex]\(3x^{11}\)[/tex]: The term with the highest power is [tex]\(x^{11}\)[/tex].
- [tex]\(9x^7\)[/tex]: The next highest power is [tex]\(x^7\)[/tex].
- [tex]\(5x^3\)[/tex]: Then, the power is [tex]\(x^3\)[/tex].
- [tex]\(-x\)[/tex]: The power of [tex]\(x\)[/tex] here is [tex]\(x^1\)[/tex].
- [tex]\(4\)[/tex]: This is a constant term with [tex]\(x^0\)[/tex].
2. Arrange Terms by Exponents:
- Write the terms in order from highest to lowest power of [tex]\(x\)[/tex]: [tex]\(3x^{11}\)[/tex], [tex]\(9x^7\)[/tex], [tex]\(5x^3\)[/tex], [tex]\(-x\)[/tex], and [tex]\(4\)[/tex].
3. Combine the Terms:
- Combine these terms into one polynomial: [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
After arranging them correctly, the polynomial in descending order is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
Therefore, the correct option from the given choices is:
- B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
