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Answer :
To determine which polynomial lists the powers in descending order, you need to rearrange each option so that the terms are ordered from highest power of [tex]\( x \)[/tex] to lowest power.
Let's analyze each option:
A. [tex]\(3 x^6 + 10 x^2 + x^8 + 8 x^3 - 2\)[/tex]:
- Rearrange in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
B. [tex]\(x^8 + 3 x^6 + 8 x^3 + 10 x^2 - 2\)[/tex]:
- This polynomial is already in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
C. [tex]\(x^8 + 10 x^2 + 8 x^3 + 3 x^6 - 2\)[/tex]:
- Rearrange in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
D. [tex]\(10 x^2 + 8 x^3 + x^8 - 2 + 3 x^6\)[/tex]:
- Rearrange in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
After rearranging all options, we see that option B is already presented in descending order with terms from highest to lowest power.
So, the correct answer is B. [tex]\(x^8 + 3 x^6 + 8 x^3 + 10 x^2 - 2\)[/tex].
Let's analyze each option:
A. [tex]\(3 x^6 + 10 x^2 + x^8 + 8 x^3 - 2\)[/tex]:
- Rearrange in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
B. [tex]\(x^8 + 3 x^6 + 8 x^3 + 10 x^2 - 2\)[/tex]:
- This polynomial is already in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
C. [tex]\(x^8 + 10 x^2 + 8 x^3 + 3 x^6 - 2\)[/tex]:
- Rearrange in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
D. [tex]\(10 x^2 + 8 x^3 + x^8 - 2 + 3 x^6\)[/tex]:
- Rearrange in descending order: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
After rearranging all options, we see that option B is already presented in descending order with terms from highest to lowest power.
So, the correct answer is B. [tex]\(x^8 + 3 x^6 + 8 x^3 + 10 x^2 - 2\)[/tex].
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