Answer :
To write the polynomial [tex]\(2x^2 - 4x + x^6 + 8 + 3x^{10}\)[/tex] in descending order, you'll want to list the terms from the highest degree to the lowest degree. Here's how you can do that:
1. Identify the terms and their degrees:
- [tex]\(3x^{10}\)[/tex]: degree 10
- [tex]\(x^6\)[/tex]: degree 6
- [tex]\(2x^2\)[/tex]: degree 2
- [tex]\(-4x\)[/tex]: degree 1
- [tex]\(8\)[/tex]: degree 0
2. Reorder the terms by their degrees, from highest to lowest:
- Start with the term with the highest degree: [tex]\(3x^{10}\)[/tex]
- Next, include the term with the second highest degree: [tex]\(x^6\)[/tex]
- Then add the term with the next degree: [tex]\(2x^2\)[/tex]
- Follow with the term of degree 1: [tex]\(-4x\)[/tex]
- Finally, add the constant term: [tex]\(8\)[/tex]
3. Put it all together:
- The polynomial in descending order is: [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex]
Among the options given, option B matches this order:
B. [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex]
Therefore, the correct answer is B.
1. Identify the terms and their degrees:
- [tex]\(3x^{10}\)[/tex]: degree 10
- [tex]\(x^6\)[/tex]: degree 6
- [tex]\(2x^2\)[/tex]: degree 2
- [tex]\(-4x\)[/tex]: degree 1
- [tex]\(8\)[/tex]: degree 0
2. Reorder the terms by their degrees, from highest to lowest:
- Start with the term with the highest degree: [tex]\(3x^{10}\)[/tex]
- Next, include the term with the second highest degree: [tex]\(x^6\)[/tex]
- Then add the term with the next degree: [tex]\(2x^2\)[/tex]
- Follow with the term of degree 1: [tex]\(-4x\)[/tex]
- Finally, add the constant term: [tex]\(8\)[/tex]
3. Put it all together:
- The polynomial in descending order is: [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex]
Among the options given, option B matches this order:
B. [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex]
Therefore, the correct answer is B.
