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Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, we need to arrange its terms from the highest degree to the lowest degree.
Here is the step-by-step process:
1. Identify the degree of each term:
- The term [tex]\(4x^{12}\)[/tex] has a degree of 12.
- The term [tex]\(9x^7\)[/tex] has a degree of 7.
- The term [tex]\(3x^3\)[/tex] has a degree of 3.
- The term [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], which has a degree of 1.
2. Arrange the terms by their degrees in descending order:
- Start with the term having the highest degree: [tex]\(4x^{12}\)[/tex].
- Follow with the next highest degree: [tex]\(9x^7\)[/tex].
- Then, the next: [tex]\(3x^3\)[/tex].
- Lastly, add the term with the lowest degree: [tex]\(-x\)[/tex].
3. Write the polynomial in descending order:
- The polynomial becomes: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Therefore, the polynomial in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Here is the step-by-step process:
1. Identify the degree of each term:
- The term [tex]\(4x^{12}\)[/tex] has a degree of 12.
- The term [tex]\(9x^7\)[/tex] has a degree of 7.
- The term [tex]\(3x^3\)[/tex] has a degree of 3.
- The term [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], which has a degree of 1.
2. Arrange the terms by their degrees in descending order:
- Start with the term having the highest degree: [tex]\(4x^{12}\)[/tex].
- Follow with the next highest degree: [tex]\(9x^7\)[/tex].
- Then, the next: [tex]\(3x^3\)[/tex].
- Lastly, add the term with the lowest degree: [tex]\(-x\)[/tex].
3. Write the polynomial in descending order:
- The polynomial becomes: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Therefore, the polynomial in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
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