Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, follow these steps:
1. Identify the Terms and Their Powers:
- [tex]\(4x^{12}\)[/tex]: This term has the highest power, 12.
- [tex]\(9x^7\)[/tex]: This term has a power of 7.
- [tex]\(3x^3\)[/tex]: This term has a power of 3.
- [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]): This term has the lowest power, 1.
2. Arrange the Terms in Descending Order of Powers:
- Start with the term with the highest power and work down to the term with the lowest power.
3. Write the Polynomial:
- In order of descending power, the polynomial is:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
4. Match This with the Given Options:
- Option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Therefore, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which corresponds to option A.
1. Identify the Terms and Their Powers:
- [tex]\(4x^{12}\)[/tex]: This term has the highest power, 12.
- [tex]\(9x^7\)[/tex]: This term has a power of 7.
- [tex]\(3x^3\)[/tex]: This term has a power of 3.
- [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]): This term has the lowest power, 1.
2. Arrange the Terms in Descending Order of Powers:
- Start with the term with the highest power and work down to the term with the lowest power.
3. Write the Polynomial:
- In order of descending power, the polynomial is:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
4. Match This with the Given Options:
- Option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Therefore, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which corresponds to option A.
