Answer :
To determine which polynomial lists the powers in descending order, let's examine each option carefully by reorganizing their terms so the exponents decrease from left to right.
Option A: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Reorder the terms:
- [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Reorder the terms:
- [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option C: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Reorder the terms:
- [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option D: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- The terms are already in descending order of exponents.
Looking at all the options, we see that Option D is already written with the powers in descending order: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex].
Therefore, Option D is the correct polynomial with powers listed in descending order.
Option A: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Reorder the terms:
- [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Reorder the terms:
- [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option C: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Reorder the terms:
- [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
Option D: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- The terms are already in descending order of exponents.
Looking at all the options, we see that Option D is already written with the powers in descending order: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex].
Therefore, Option D is the correct polynomial with powers listed in descending order.
