Answer :
To write the polynomial in descending order, we need to organize the terms based on the powers of [tex]\(x\)[/tex], starting from the highest to the lowest power. Let's go through the steps:
1. Identify the powers of [tex]\(x\)[/tex] in each term:
- [tex]\(4x^{12}\)[/tex] has a power of 12.
- [tex]\(9x^7\)[/tex] has a power of 7.
- [tex]\(3x^3\)[/tex] has a power of 3.
- [tex]\(-x\)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex], so it has a power of 1.
2. List the terms in order of their powers from highest to lowest:
- The highest power is 12, which corresponds to the term [tex]\(4x^{12}\)[/tex].
- The next highest power is 7, which corresponds to the term [tex]\(9x^7\)[/tex].
- After that, we have the power of 3, corresponding to the term [tex]\(3x^3\)[/tex].
- Finally, we have the power of 1, corresponding to the term [tex]\(-x\)[/tex].
3. Write the polynomial with the terms in descending order:
So, the polynomial in descending order is:
[tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
4. Select the correct choice that matches this order:
The choice that corresponds to this order is:
A. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Thus, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches choice A.
1. Identify the powers of [tex]\(x\)[/tex] in each term:
- [tex]\(4x^{12}\)[/tex] has a power of 12.
- [tex]\(9x^7\)[/tex] has a power of 7.
- [tex]\(3x^3\)[/tex] has a power of 3.
- [tex]\(-x\)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex], so it has a power of 1.
2. List the terms in order of their powers from highest to lowest:
- The highest power is 12, which corresponds to the term [tex]\(4x^{12}\)[/tex].
- The next highest power is 7, which corresponds to the term [tex]\(9x^7\)[/tex].
- After that, we have the power of 3, corresponding to the term [tex]\(3x^3\)[/tex].
- Finally, we have the power of 1, corresponding to the term [tex]\(-x\)[/tex].
3. Write the polynomial with the terms in descending order:
So, the polynomial in descending order is:
[tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
4. Select the correct choice that matches this order:
The choice that corresponds to this order is:
A. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Thus, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches choice A.
