Answer :
To determine which polynomial lists the powers in descending order, let's first understand what descending order means. It involves arranging the exponents of a polynomial from highest to lowest.
Let's assess each option:
Option A: [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]
1. Identify the terms: [tex]\(3x^6\)[/tex], [tex]\(10x^2\)[/tex], [tex]\(x^8\)[/tex], [tex]\(8x^3\)[/tex], and [tex]\(-2\)[/tex].
2. List the powers: [tex]\(6, 2, 8, 3, 0\)[/tex].
3. Rearrange terms by power in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
Option B: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
1. Identify the terms: [tex]\(x^8\)[/tex], [tex]\(3x^6\)[/tex], [tex]\(8x^3\)[/tex], [tex]\(10x^2\)[/tex], and [tex]\(-2\)[/tex].
2. List the powers: [tex]\(8, 6, 3, 2, 0\)[/tex].
3. This is already in descending order.
Option C: [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]
1. Identify the terms: [tex]\(x^8\)[/tex], [tex]\(10x^2\)[/tex], [tex]\(8x^3\)[/tex], [tex]\(3x^6\)[/tex], and [tex]\(-2\)[/tex].
2. List the powers: [tex]\(8, 2, 3, 6, 0\)[/tex].
3. Rearrange terms by power in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
Option D: [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]
1. Identify the terms: [tex]\(10x^2\)[/tex], [tex]\(8x^3\)[/tex], [tex]\(x^8\)[/tex], [tex]\(-2\)[/tex], and [tex]\(3x^6\)[/tex].
2. List the powers: [tex]\(2, 3, 8, 0, 6\)[/tex].
3. Rearrange terms by power in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
After examining each option:
- Option B is already correctly listed with powers in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
Therefore, the correct polynomial in descending order is from Option B.
Let's assess each option:
Option A: [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]
1. Identify the terms: [tex]\(3x^6\)[/tex], [tex]\(10x^2\)[/tex], [tex]\(x^8\)[/tex], [tex]\(8x^3\)[/tex], and [tex]\(-2\)[/tex].
2. List the powers: [tex]\(6, 2, 8, 3, 0\)[/tex].
3. Rearrange terms by power in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
Option B: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
1. Identify the terms: [tex]\(x^8\)[/tex], [tex]\(3x^6\)[/tex], [tex]\(8x^3\)[/tex], [tex]\(10x^2\)[/tex], and [tex]\(-2\)[/tex].
2. List the powers: [tex]\(8, 6, 3, 2, 0\)[/tex].
3. This is already in descending order.
Option C: [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]
1. Identify the terms: [tex]\(x^8\)[/tex], [tex]\(10x^2\)[/tex], [tex]\(8x^3\)[/tex], [tex]\(3x^6\)[/tex], and [tex]\(-2\)[/tex].
2. List the powers: [tex]\(8, 2, 3, 6, 0\)[/tex].
3. Rearrange terms by power in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
Option D: [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]
1. Identify the terms: [tex]\(10x^2\)[/tex], [tex]\(8x^3\)[/tex], [tex]\(x^8\)[/tex], [tex]\(-2\)[/tex], and [tex]\(3x^6\)[/tex].
2. List the powers: [tex]\(2, 3, 8, 0, 6\)[/tex].
3. Rearrange terms by power in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
After examining each option:
- Option B is already correctly listed with powers in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
Therefore, the correct polynomial in descending order is from Option B.
