College

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

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

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

Answer :

To write the polynomial in descending order, we need to arrange the terms from highest to lowest degree according to their exponents.

Here’s the given polynomial:

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

Let's identify the terms and their degrees:

1. [tex]\(2x^{10}\)[/tex] has degree 10.
2. [tex]\(8x^6\)[/tex] has degree 6.
3. [tex]\(4x^2\)[/tex] has degree 2.
4. [tex]\(-x\)[/tex] has degree 1.
5. The constant term [tex]\(3\)[/tex] has degree 0.

Now, we arrange these terms in descending order of their degrees:

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

Putting them together, the polynomial in descending order is:

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

This matches option C:

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

Therefore, the correct choice is C.

Other Questions