Answer :
Sure! Let's go through each option to see which polynomial has its powers listed in descending order.
To arrange the terms of a polynomial in descending order, you should start from the term with the highest power of [tex]\(x\)[/tex] and go down to the lowest.
Let's evaluate each option:
Option A: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- The powers are: 2, 3, 8, 0, 6
- This is not in descending order.
Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- The powers are: 6, 2, 8, 3, 0
- This is not in descending order.
Option C: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- The powers are: 8, 6, 3, 2, 0
- This is correctly in descending order.
Option D: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- The powers are: 8, 2, 3, 6, 0
- This is not in descending order.
Based on our evaluation, Option C is the correct answer, as it lists the polynomial terms from the highest power to the lowest power.
So, the correct polynomial with powers in descending order is: Option C: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex].
To arrange the terms of a polynomial in descending order, you should start from the term with the highest power of [tex]\(x\)[/tex] and go down to the lowest.
Let's evaluate each option:
Option A: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- The powers are: 2, 3, 8, 0, 6
- This is not in descending order.
Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- The powers are: 6, 2, 8, 3, 0
- This is not in descending order.
Option C: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- The powers are: 8, 6, 3, 2, 0
- This is correctly in descending order.
Option D: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- The powers are: 8, 2, 3, 6, 0
- This is not in descending order.
Based on our evaluation, Option C is the correct answer, as it lists the polynomial terms from the highest power to the lowest power.
So, the correct polynomial with powers in descending order is: Option C: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex].
