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Answer :
To write the polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order, you need to arrange the terms based on the powers of [tex]\(x\)[/tex], starting with the highest power down to the lowest. Here’s how we can do it step-by-step:
1. Identify the terms:
- The polynomial has the terms:
- [tex]\(3x^{11}\)[/tex] (with power 11)
- [tex]\(9x^7\)[/tex] (with power 7)
- [tex]\(5x^3\)[/tex] (with power 3)
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex], with power 1)
- [tex]\(4\)[/tex] (which is a constant, or [tex]\(4x^0\)[/tex], with power 0)
2. Order the terms by descending power:
- Start with the highest power and work downwards:
- [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] (next, power 1)
- [tex]\(4\)[/tex] (constant, power 0)
3. Write the polynomial in descending order:
- Combine the ordered terms:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
Thus, the polynomial written in descending order according to the powers of [tex]\(x\)[/tex] is:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
Comparing with the given choices, the correct option is D. [tex]\(3 x^{11} + 9 x^7 + 5 x^3 - x + 4\)[/tex].
1. Identify the terms:
- The polynomial has the terms:
- [tex]\(3x^{11}\)[/tex] (with power 11)
- [tex]\(9x^7\)[/tex] (with power 7)
- [tex]\(5x^3\)[/tex] (with power 3)
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex], with power 1)
- [tex]\(4\)[/tex] (which is a constant, or [tex]\(4x^0\)[/tex], with power 0)
2. Order the terms by descending power:
- Start with the highest power and work downwards:
- [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] (next, power 1)
- [tex]\(4\)[/tex] (constant, power 0)
3. Write the polynomial in descending order:
- Combine the ordered terms:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
Thus, the polynomial written in descending order according to the powers of [tex]\(x\)[/tex] is:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
Comparing with the given choices, the correct option is D. [tex]\(3 x^{11} + 9 x^7 + 5 x^3 - x + 4\)[/tex].
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