Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, you need to arrange the terms based on the degree of each term, from the highest exponent to the lowest. Let's break it down:
1. Identify the Degree of Each Term:
- [tex]\(4x^{12}\)[/tex] has a degree of 12.
- [tex]\(9x^7\)[/tex] has a degree of 7.
- [tex]\(3x^3\)[/tex] has a degree of 3.
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex]) has a degree of 1.
2. Arrange the Terms in Descending Order:
- The term with the highest degree is [tex]\(4x^{12}\)[/tex].
- The next highest degree term is [tex]\(9x^7\)[/tex].
- Next is [tex]\(3x^3\)[/tex].
- The lowest degree term is [tex]\(-x\)[/tex].
So, the polynomial in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
3. Match with the given options:
- Option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Therefore, the correct answer is Option A.
1. Identify the Degree of Each Term:
- [tex]\(4x^{12}\)[/tex] has a degree of 12.
- [tex]\(9x^7\)[/tex] has a degree of 7.
- [tex]\(3x^3\)[/tex] has a degree of 3.
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex]) has a degree of 1.
2. Arrange the Terms in Descending Order:
- The term with the highest degree is [tex]\(4x^{12}\)[/tex].
- The next highest degree term is [tex]\(9x^7\)[/tex].
- Next is [tex]\(3x^3\)[/tex].
- The lowest degree term is [tex]\(-x\)[/tex].
So, the polynomial in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
3. Match with the given options:
- Option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Therefore, the correct answer is Option A.
