Answer :
To write the polynomial [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex] in descending order, we need to arrange the terms from the highest power of [tex]\(x\)[/tex] to the lowest power. Here's how you can do it step by step:
1. Identify the powers of [tex]\(x\)[/tex] in each term:
- The term [tex]\(4x^2\)[/tex] has a power of 2.
- The term [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x\)[/tex]) has a power of 1.
- The term [tex]\(8x^6\)[/tex] has a power of 6.
- The term [tex]\(3\)[/tex] is constant, which can be thought of as having a power of 0.
- The term [tex]\(2x^{10}\)[/tex] has a power of 10.
2. Arrange the terms in order from the highest power to the lowest power:
- Start with the term that has the highest power, which is [tex]\(2x^{10}\)[/tex].
- Next, use the term with the next highest power, which is [tex]\(8x^6\)[/tex].
- Follow it with [tex]\(4x^2\)[/tex], then [tex]\(-x\)[/tex], and finally the constant [tex]\(3\)[/tex].
3. Write down the reordered polynomial:
- Putting it all together, the polynomial in descending order is:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
So, the polynomial in descending order is option A: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
1. Identify the powers of [tex]\(x\)[/tex] in each term:
- The term [tex]\(4x^2\)[/tex] has a power of 2.
- The term [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x\)[/tex]) has a power of 1.
- The term [tex]\(8x^6\)[/tex] has a power of 6.
- The term [tex]\(3\)[/tex] is constant, which can be thought of as having a power of 0.
- The term [tex]\(2x^{10}\)[/tex] has a power of 10.
2. Arrange the terms in order from the highest power to the lowest power:
- Start with the term that has the highest power, which is [tex]\(2x^{10}\)[/tex].
- Next, use the term with the next highest power, which is [tex]\(8x^6\)[/tex].
- Follow it with [tex]\(4x^2\)[/tex], then [tex]\(-x\)[/tex], and finally the constant [tex]\(3\)[/tex].
3. Write down the reordered polynomial:
- Putting it all together, the polynomial in descending order is:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
So, the polynomial in descending order is option A: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
