Sure, let's determine which polynomial lists the powers in descending order step-by-step:
Given options:
1. [tex]\( A. 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
2. [tex]\( B. 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
3. [tex]\( C. x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
4. [tex]\( D. x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
We'll check each option to see if it lists the powers of [tex]\( x \)[/tex] in descending order:
### Option A: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Powers: 2, 3, 8, 0 (constant term), 6.
- Order: 2, 3, 8, 0, 6 (not in descending order).
### Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Powers: 6, 2, 8, 3, 0 (constant term).
- Order: 6, 2, 8, 3, 0 (not in descending order).
### Option C: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- Powers: 8, 6, 3, 2, 0 (constant term).
- Order: 8, 6, 3, 2, 0 (in descending order).
### Option D: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Powers: 8, 2, 3, 6, 0 (constant term).
- Order: 8, 2, 3, 6, 0 (not in descending order).
From these observations:
- Option A does not list the powers in descending order.
- Option B does not list the powers in descending order.
- Option C lists the powers in descending order.
- Option D does not list the powers in descending order.
Therefore, the polynomial that lists the powers in descending order is:
[tex]\[ \boxed{\text{C}} \][/tex]
