Answer :
To identify which polynomial lists the powers in descending order, we need to examine the exponents of [tex]\(x\)[/tex] in each polynomial and ensure they decrease from left to right.
Option A: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- The powers of [tex]\(x\)[/tex] are [tex]\(6, 2, 8, 3, 0\)[/tex].
- These powers are not in descending order.
Option B: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- The powers of [tex]\(x\)[/tex] are [tex]\(8, 2, 3, 6, 0\)[/tex].
- These 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 [tex]\(2, 3, 8, 0, 6\)[/tex].
- These powers are not in descending order.
Option D: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- The powers of [tex]\(x\)[/tex] are [tex]\(8, 6, 3, 2, 0\)[/tex].
- These powers are in descending order.
Therefore, the polynomial that lists the powers in descending order is:
D. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option A: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- The powers of [tex]\(x\)[/tex] are [tex]\(6, 2, 8, 3, 0\)[/tex].
- These powers are not in descending order.
Option B: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- The powers of [tex]\(x\)[/tex] are [tex]\(8, 2, 3, 6, 0\)[/tex].
- These 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 [tex]\(2, 3, 8, 0, 6\)[/tex].
- These powers are not in descending order.
Option D: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- The powers of [tex]\(x\)[/tex] are [tex]\(8, 6, 3, 2, 0\)[/tex].
- These powers are in descending order.
Therefore, the polynomial that lists the powers in descending order is:
D. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
