Answer :
To write the polynomial [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex] in descending order, you'll want to arrange the terms from the highest degree to the lowest degree. Here's how we do it step by step:
1. Identify the degrees of each term:
- [tex]\(2x^{10}\)[/tex] has a degree of 10.
- [tex]\(8x^6\)[/tex] has a degree of 6.
- [tex]\(4x^2\)[/tex] has a degree of 2.
- [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x^1\)[/tex]) has a degree of 1.
- The constant [tex]\(3\)[/tex] has a degree of 0.
2. Order the terms by degree from highest to lowest:
- Start with the term with the highest degree: [tex]\(2x^{10}\)[/tex].
- Next is the term with the degree of 6: [tex]\(8x^6\)[/tex].
- After that, include the term with degree 2: [tex]\(4x^2\)[/tex].
- Then the term with degree 1: [tex]\(-x\)[/tex].
- Finally, the constant term [tex]\(3\)[/tex].
3. Write them in order:
- The polynomial in descending order is: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
Now, let's look at the options provided:
- A. [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
- B. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
- C. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- D. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
By comparing these, you can see that option D matches the polynomial arranged in descending order. So, the correct answer is D: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
1. Identify the degrees of each term:
- [tex]\(2x^{10}\)[/tex] has a degree of 10.
- [tex]\(8x^6\)[/tex] has a degree of 6.
- [tex]\(4x^2\)[/tex] has a degree of 2.
- [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x^1\)[/tex]) has a degree of 1.
- The constant [tex]\(3\)[/tex] has a degree of 0.
2. Order the terms by degree from highest to lowest:
- Start with the term with the highest degree: [tex]\(2x^{10}\)[/tex].
- Next is the term with the degree of 6: [tex]\(8x^6\)[/tex].
- After that, include the term with degree 2: [tex]\(4x^2\)[/tex].
- Then the term with degree 1: [tex]\(-x\)[/tex].
- Finally, the constant term [tex]\(3\)[/tex].
3. Write them in order:
- The polynomial in descending order is: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
Now, let's look at the options provided:
- A. [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
- B. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
- C. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- D. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
By comparing these, you can see that option D matches the polynomial arranged in descending order. So, the correct answer is D: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
