Answer :
To write a polynomial in descending order, we arrange its terms by the powers of [tex]\(x\)[/tex], starting from the highest to the lowest. Here's how to do it for the polynomial given:
Original polynomial: [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex].
Step 1: Identify the terms and their exponents.
- The terms with their powers are:
- [tex]\(2x^{10}\)[/tex] (highest power is 10)
- [tex]\(8x^6\)[/tex] (power is 6)
- [tex]\(4x^2\)[/tex] (power is 2)
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex], power is 1)
- [tex]\(3\)[/tex] (constant term, power is 0)
Step 2: Arrange the terms in order of decreasing powers of [tex]\(x\)[/tex].
- Start with the term with the highest power: [tex]\(2x^{10}\)[/tex].
- Then the next highest power: [tex]\(8x^6\)[/tex].
- Followed by: [tex]\(4x^2\)[/tex].
- Next is: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\(3\)[/tex].
Step 3: Write the polynomial in the correct order.
- Putting it all together, the polynomial in descending order is:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
Comparing this with the options given:
- Option A: [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- Option B: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
- Option C: [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
- Option D: [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
The correct answer is Option B: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
Original polynomial: [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex].
Step 1: Identify the terms and their exponents.
- The terms with their powers are:
- [tex]\(2x^{10}\)[/tex] (highest power is 10)
- [tex]\(8x^6\)[/tex] (power is 6)
- [tex]\(4x^2\)[/tex] (power is 2)
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex], power is 1)
- [tex]\(3\)[/tex] (constant term, power is 0)
Step 2: Arrange the terms in order of decreasing powers of [tex]\(x\)[/tex].
- Start with the term with the highest power: [tex]\(2x^{10}\)[/tex].
- Then the next highest power: [tex]\(8x^6\)[/tex].
- Followed by: [tex]\(4x^2\)[/tex].
- Next is: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\(3\)[/tex].
Step 3: Write the polynomial in the correct order.
- Putting it all together, the polynomial in descending order is:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
Comparing this with the options given:
- Option A: [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- Option B: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
- Option C: [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
- Option D: [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
The correct answer is Option B: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
