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Answer :
To determine which polynomial lists the powers in descending order, we'll examine each option one by one and check the order of the exponents.
Option A:
[tex]\[ x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \][/tex]
- The exponents of [tex]\(x\)[/tex] are: [tex]\(8, 6, 3, 2, 0\)[/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 exponents of [tex]\(x\)[/tex] are: [tex]\(6, 2, 8, 3, 0\)[/tex].
- The powers are not in descending order because [tex]\(8\)[/tex] comes after [tex]\(6\)[/tex].
Option C:
[tex]\[ x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \][/tex]
- The exponents of [tex]\(x\)[/tex] are: [tex]\(8, 2, 3, 6, 0\)[/tex].
- The powers are not in descending order because [tex]\(3\)[/tex] and [tex]\(6\)[/tex] come after [tex]\(2\)[/tex].
Option D:
[tex]\[ 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \][/tex]
- The exponents of [tex]\(x\)[/tex] are: [tex]\(2, 3, 8, 0, 6\)[/tex].
- The powers are not in descending order because [tex]\(8\)[/tex] comes after [tex]\(3\)[/tex].
The polynomial in option A is the only one where the exponents of [tex]\(x\)[/tex] are in descending order: [tex]\(8, 6, 3, 2, 0\)[/tex].
Therefore, the correct answer is Option A.
Option A:
[tex]\[ x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \][/tex]
- The exponents of [tex]\(x\)[/tex] are: [tex]\(8, 6, 3, 2, 0\)[/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 exponents of [tex]\(x\)[/tex] are: [tex]\(6, 2, 8, 3, 0\)[/tex].
- The powers are not in descending order because [tex]\(8\)[/tex] comes after [tex]\(6\)[/tex].
Option C:
[tex]\[ x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \][/tex]
- The exponents of [tex]\(x\)[/tex] are: [tex]\(8, 2, 3, 6, 0\)[/tex].
- The powers are not in descending order because [tex]\(3\)[/tex] and [tex]\(6\)[/tex] come after [tex]\(2\)[/tex].
Option D:
[tex]\[ 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \][/tex]
- The exponents of [tex]\(x\)[/tex] are: [tex]\(2, 3, 8, 0, 6\)[/tex].
- The powers are not in descending order because [tex]\(8\)[/tex] comes after [tex]\(3\)[/tex].
The polynomial in option A is the only one where the exponents of [tex]\(x\)[/tex] are in descending order: [tex]\(8, 6, 3, 2, 0\)[/tex].
Therefore, the correct answer is Option A.
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