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Which polynomial lists the powers in descending order?

A. [tex][tex]$10 x^2+8 x^3+x^8-2+3 x^6$[/tex][/tex]

B. [tex][tex]$3 x^6+10 x^2+x^8+8 x^3-2$[/tex][/tex]

C. [tex][tex]$x^8+3 x^6+8 x^3+10 x^2-2$[/tex][/tex]

D. [tex][tex]$x^8+10 x^2+8 x^3+3 x^6-2$[/tex][/tex]



Answer :

GinnyAnswer
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]

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