Answer :
To write a polynomial in descending order, you arrange the terms from the highest degree to the lowest degree. Here's how you can do that for the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex]:
1. Identify the degrees 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] has a degree of 1.
2. Order the terms by descending power:
Start with the term that has the highest degree and proceed to the lowest.
3. Re-order the polynomial:
Begin with [tex]\(4x^{12}\)[/tex] as it has the highest degree, followed by [tex]\(9x^7\)[/tex], then [tex]\(3x^3\)[/tex], and finally [tex]\(-x\)[/tex].
Putting it all together, the polynomial in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Therefore, the correct choice is:
C. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
1. Identify the degrees 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] has a degree of 1.
2. Order the terms by descending power:
Start with the term that has the highest degree and proceed to the lowest.
3. Re-order the polynomial:
Begin with [tex]\(4x^{12}\)[/tex] as it has the highest degree, followed by [tex]\(9x^7\)[/tex], then [tex]\(3x^3\)[/tex], and finally [tex]\(-x\)[/tex].
Putting it all together, the polynomial in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Therefore, the correct choice is:
C. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
