Answer :
To solve this question, we need to identify which polynomial lists the powers of [tex]\(x\)[/tex] in descending order. Let's check each option one by one:
A. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(8, 6, 3, 2, 0\)[/tex].
- This is in descending order.
B. [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(6, 2, 8, 3, 0\)[/tex].
- This is not in descending order (8 should come before 6).
C. [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(8, 2, 3, 6, 0\)[/tex].
- This is not in descending order (order should be 8, 6, 3, 2, 0).
D. [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(2, 3, 8, 0, 6\)[/tex].
- This is not in descending order.
Among the options, Option A lists the powers in descending order. Therefore, the correct answer is A. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
A. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(8, 6, 3, 2, 0\)[/tex].
- This is in descending order.
B. [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(6, 2, 8, 3, 0\)[/tex].
- This is not in descending order (8 should come before 6).
C. [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(8, 2, 3, 6, 0\)[/tex].
- This is not in descending order (order should be 8, 6, 3, 2, 0).
D. [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]:
- Powers of [tex]\(x\)[/tex] are: [tex]\(2, 3, 8, 0, 6\)[/tex].
- This is not in descending order.
Among the options, Option A lists the powers in descending order. Therefore, the correct answer is A. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex].
