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Answer :
To determine which polynomial lists the powers in descending order, let's analyze each option carefully:
Option A: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 8, 6, 3, 2, and the constant term -2 (which is [tex]\(x^0\)[/tex]).
- The powers are in descending order: [tex]\(8, 6, 3, 2, 0\)[/tex].
Option B: [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 6, 2, 8, 3, and the constant term -2 (which is [tex]\(x^0\)[/tex]).
- The powers are not in descending order.
Option C: [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 2, 3, 8, and the constant term -2 (which is [tex]\(x^0\)[/tex], and then 6).
- The powers are not in descending order.
Option D: [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 8, 2, 3, 6, and the constant term -2 (which is [tex]\(x^0\)[/tex]).
- The powers are not in descending order.
After examining each option, we see that Option A is the only polynomial where the powers of [tex]\(x\)[/tex] are in descending order. Thus, the correct answer is:
Option A: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
Option A: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 8, 6, 3, 2, and the constant term -2 (which is [tex]\(x^0\)[/tex]).
- The powers are in descending order: [tex]\(8, 6, 3, 2, 0\)[/tex].
Option B: [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 6, 2, 8, 3, and the constant term -2 (which is [tex]\(x^0\)[/tex]).
- The powers are not in descending order.
Option C: [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 2, 3, 8, and the constant term -2 (which is [tex]\(x^0\)[/tex], and then 6).
- The powers are not in descending order.
Option D: [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]
- The powers of [tex]\(x\)[/tex] are: 8, 2, 3, 6, and the constant term -2 (which is [tex]\(x^0\)[/tex]).
- The powers are not in descending order.
After examining each option, we see that Option A is the only polynomial where the powers of [tex]\(x\)[/tex] are in descending order. Thus, the correct answer is:
Option A: [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
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