Answer :
To write the polynomial in descending order, we need to arrange the terms by the exponents of [tex]\(x\)[/tex] in decreasing order. Let's work through the process step-by-step:
1. Identify the Terms and Exponents:
- [tex]\(4x^{12}\)[/tex] has an exponent of 12.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(3x^3\)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex], which has an exponent of 1.
2. Arrange Terms by Decreasing Exponents:
Start with the term with the highest exponent and proceed to the lowest:
- The highest exponent is 12, so we start with [tex]\(4x^{12}\)[/tex].
- Next is the exponent 7, so we add [tex]\(9x^7\)[/tex].
- Then comes the exponent 3, for [tex]\(3x^3\)[/tex].
- Finally, the lowest exponent is 1, so we end with [tex]\(-x\)[/tex].
3. Construct the Polynomial:
Put these terms together in their new order:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
This matches option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]. Therefore, the polynomial written in descending order is:
A. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
1. Identify the Terms and Exponents:
- [tex]\(4x^{12}\)[/tex] has an exponent of 12.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(3x^3\)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex], which has an exponent of 1.
2. Arrange Terms by Decreasing Exponents:
Start with the term with the highest exponent and proceed to the lowest:
- The highest exponent is 12, so we start with [tex]\(4x^{12}\)[/tex].
- Next is the exponent 7, so we add [tex]\(9x^7\)[/tex].
- Then comes the exponent 3, for [tex]\(3x^3\)[/tex].
- Finally, the lowest exponent is 1, so we end with [tex]\(-x\)[/tex].
3. Construct the Polynomial:
Put these terms together in their new order:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
This matches option A: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]. Therefore, the polynomial written in descending order is:
A. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
