Answer :
To write the polynomial [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex] in descending order, follow these steps:
1. Identify the Polynomial Terms and Their Exponents:
- [tex]\(4x^2\)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] with an exponent of 1.
- [tex]\(8x^6\)[/tex] has an exponent of 6.
- [tex]\(3\)[/tex] is a constant term with an implied exponent of 0.
- [tex]\(2x^{10}\)[/tex] has an exponent of 10.
2. Arrange the Terms by Exponents in Descending Order:
- Start with the term having the highest exponent and move to the lowest.
- The highest exponent here is 10 from the term [tex]\(2x^{10}\)[/tex].
- Next is the exponent 6 from the term [tex]\(8x^6\)[/tex].
- Then comes the exponent 2 from the term [tex]\(4x^2\)[/tex].
- Followed by the exponent 1 from the term [tex]\(-x\)[/tex].
- Finally, add the constant term [tex]\(3\)[/tex].
3. Write the Polynomial with Terms in Order:
- Combine these terms, starting with the highest exponent first.
- The ordered polynomial is: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
Based on this order, the correct representation of the polynomial in descending order is:
[tex]\[ \boxed{2x^{10} + 8x^6 + 4x^2 - x + 3} \][/tex]
This arrangement matches option A in the question.
1. Identify the Polynomial Terms and Their Exponents:
- [tex]\(4x^2\)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] with an exponent of 1.
- [tex]\(8x^6\)[/tex] has an exponent of 6.
- [tex]\(3\)[/tex] is a constant term with an implied exponent of 0.
- [tex]\(2x^{10}\)[/tex] has an exponent of 10.
2. Arrange the Terms by Exponents in Descending Order:
- Start with the term having the highest exponent and move to the lowest.
- The highest exponent here is 10 from the term [tex]\(2x^{10}\)[/tex].
- Next is the exponent 6 from the term [tex]\(8x^6\)[/tex].
- Then comes the exponent 2 from the term [tex]\(4x^2\)[/tex].
- Followed by the exponent 1 from the term [tex]\(-x\)[/tex].
- Finally, add the constant term [tex]\(3\)[/tex].
3. Write the Polynomial with Terms in Order:
- Combine these terms, starting with the highest exponent first.
- The ordered polynomial is: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
Based on this order, the correct representation of the polynomial in descending order is:
[tex]\[ \boxed{2x^{10} + 8x^6 + 4x^2 - x + 3} \][/tex]
This arrangement matches option A in the question.
