College

Which polynomial lists the powers in descending order?

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

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

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

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

Answer :

To determine which polynomial lists the powers in descending order, we need to analyze each option and arrange the terms from the highest power of [tex]\( x \)[/tex] to the lowest.

Let's look at the options:

A. [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Examine the powers: 6, 2, 8, 3, and 0 (constant term has no [tex]\( x \)[/tex] power).
- This is not in descending order as the term [tex]\( x^8 \)[/tex] should be first.

B. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- Examine the powers: 8, 6, 3, 2, and 0.
- The powers are in descending order from highest to lowest.

C. [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Examine the powers: 8, 2, 3, 6, and 0.
- The powers are not in descending order.

D. [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Examine the powers: 2, 3, 8, 0, and 6.
- The powers are not in descending order.

The correct polynomial, where the powers of [tex]\( x \)[/tex] are listed from highest to lowest, is:

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

This sequence is [tex]\[ 8, 6, 3, 2, 0 \][/tex], which is in strict descending order.