College

Which of the following shows the polynomial below written in descending order?

[tex]2x^2 - 4x + x^6 + 8 + 3x^{10}[/tex]

A. [tex]3x^{10} + 2x^2 - 4x + 8 + x^6[/tex]
B. [tex]3x^{10} + x^6 + 2x^2 - 4x + 8[/tex]
C. [tex]8 + 3x^{10} + x^6 + 2x^2 - 4x[/tex]
D. [tex]x^5 + 2x^2 + 8 + 3x^{10} - 4x[/tex]

Answer :

To write a polynomial in descending order, we need to arrange its terms from the highest power of [tex]\( x \)[/tex] to the lowest power of [tex]\( x \)[/tex].

Given the polynomial:
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]

Step-by-step, we identify the powers of [tex]\( x \)[/tex] in each term:
- The term [tex]\( 2x^2 \)[/tex] has a power of 2.
- The term [tex]\( -4x \)[/tex] has a power of 1.
- The term [tex]\( x^6 \)[/tex] has a power of 6.
- The term [tex]\( 8 \)[/tex] has a power of 0 (since there is no [tex]\( x \)[/tex]).
- The term [tex]\( 3x^{10} \)[/tex] has a power of 10.

Next, we arrange these terms in descending order by their powers of [tex]\( x \)[/tex]:
- The highest power is [tex]\( 10 \)[/tex], so [tex]\( 3x^{10} \)[/tex] comes first.
- The next highest power is [tex]\( 6 \)[/tex], so [tex]\( x^6 \)[/tex] comes next.
- The next highest power is [tex]\( 2 \)[/tex], so [tex]\( 2x^2 \)[/tex] comes next.
- The next highest power is [tex]\( 1 \)[/tex], so [tex]\( -4x \)[/tex] comes next.
- The lowest power is [tex]\( 0 \)[/tex], so [tex]\( 8 \)[/tex] comes last.

So, the polynomial in descending order is:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]

Among the options given, this matches option B:

B. [tex]\( 3x^{10} + x^6 + 2x^2 - 4x + 8 \)[/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]