High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which polynomial lists the powers in descending order?

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

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

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

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

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].