Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, we need to arrange the terms based on the highest power of [tex]\(x\)[/tex] first, followed by the next highest, and so on. Here's how you can do it:
1. Identify the powers of [tex]\(x\)[/tex]:
- [tex]\(3x^3\)[/tex] has a power of 3.
- [tex]\(9x^7\)[/tex] has a power of 7.
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex]) has a power of 1.
- [tex]\(4x^{12}\)[/tex] has a power of 12.
2. Sort the terms in descending order by their powers:
- The term with the highest power is [tex]\(4x^{12}\)[/tex].
- The next highest power is [tex]\(9x^7\)[/tex].
- Following that, is [tex]\(3x^3\)[/tex].
- Finally, the lowest power is [tex]\(-x\)[/tex].
3. Write the polynomial in descending order:
- The ordered polynomial is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Now, let's match this with the given options:
A. [tex]\(9 x^7 + 4 x^{12} + 3 x^3 - x\)[/tex] - Incorrect order
B. [tex]\(3 x^3 + 4 x^{12} + 9 x^7 - x\)[/tex] - Incorrect order
C. [tex]\(4 x^{12} + 9 x^7 + 3 x^3 - x\)[/tex] - Correct order
D. [tex]\(4 x^{12} + 3 x^3 - x + 9 x^7\)[/tex] - Incorrect order
The correct answer is C. [tex]\(4 x^{12} + 9 x^7 + 3 x^3 - x\)[/tex].
1. Identify the powers of [tex]\(x\)[/tex]:
- [tex]\(3x^3\)[/tex] has a power of 3.
- [tex]\(9x^7\)[/tex] has a power of 7.
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex]) has a power of 1.
- [tex]\(4x^{12}\)[/tex] has a power of 12.
2. Sort the terms in descending order by their powers:
- The term with the highest power is [tex]\(4x^{12}\)[/tex].
- The next highest power is [tex]\(9x^7\)[/tex].
- Following that, is [tex]\(3x^3\)[/tex].
- Finally, the lowest power is [tex]\(-x\)[/tex].
3. Write the polynomial in descending order:
- The ordered polynomial is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Now, let's match this with the given options:
A. [tex]\(9 x^7 + 4 x^{12} + 3 x^3 - x\)[/tex] - Incorrect order
B. [tex]\(3 x^3 + 4 x^{12} + 9 x^7 - x\)[/tex] - Incorrect order
C. [tex]\(4 x^{12} + 9 x^7 + 3 x^3 - x\)[/tex] - Correct order
D. [tex]\(4 x^{12} + 3 x^3 - x + 9 x^7\)[/tex] - Incorrect order
The correct answer is C. [tex]\(4 x^{12} + 9 x^7 + 3 x^3 - x\)[/tex].
