Answer :
To write the polynomial [tex]\(2x^2 - 4x + x^6 + 8 + 3x^{10}\)[/tex] in descending order, we want to arrange the terms from the highest power of [tex]\(x\)[/tex] to the lowest power. Let's go through each step:
1. Identify the powers of each term.
- [tex]\(3x^{10}\)[/tex] has the power 10.
- [tex]\(x^6\)[/tex] has the power 6.
- [tex]\(2x^2\)[/tex] has the power 2.
- [tex]\(-4x\)[/tex] has the power 1.
- [tex]\(8\)[/tex] is a constant term, with the power 0.
2. List the terms by descending powers.
Start with the highest power (10) and go down to the lowest power:
- First is [tex]\(3x^{10}\)[/tex].
- Then comes [tex]\(x^6\)[/tex].
- Next is [tex]\(2x^2\)[/tex].
- Followed by [tex]\(-4x\)[/tex].
- Finally, the constant [tex]\(8\)[/tex].
3. Write the polynomial in descending order.
Combine the terms in the order from Step 2:
[tex]\[
3x^{10} + x^6 + 2x^2 - 4x + 8
\][/tex]
4. Match with the given options.
According to the options provided:
- Option A is [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex].
This matches our rearranged polynomial. Therefore, the polynomial in descending order is written as [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex], and the correct answer is Option A.
1. Identify the powers of each term.
- [tex]\(3x^{10}\)[/tex] has the power 10.
- [tex]\(x^6\)[/tex] has the power 6.
- [tex]\(2x^2\)[/tex] has the power 2.
- [tex]\(-4x\)[/tex] has the power 1.
- [tex]\(8\)[/tex] is a constant term, with the power 0.
2. List the terms by descending powers.
Start with the highest power (10) and go down to the lowest power:
- First is [tex]\(3x^{10}\)[/tex].
- Then comes [tex]\(x^6\)[/tex].
- Next is [tex]\(2x^2\)[/tex].
- Followed by [tex]\(-4x\)[/tex].
- Finally, the constant [tex]\(8\)[/tex].
3. Write the polynomial in descending order.
Combine the terms in the order from Step 2:
[tex]\[
3x^{10} + x^6 + 2x^2 - 4x + 8
\][/tex]
4. Match with the given options.
According to the options provided:
- Option A is [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex].
This matches our rearranged polynomial. Therefore, the polynomial in descending order is written as [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex], and the correct answer is Option A.
