High School

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

[tex]3x^3 + 9x^7 - x + 4x^{12}[/tex]

A. [tex]4x^{12} + 9x^7 + 3x^3 - x[/tex]
B. [tex]3x^3 + 4x^{12} + 9x^7 - x[/tex]
C. [tex]4x^{12} + 3x^3 - x + 9x^7[/tex]
D. [tex]9x^7 + 4x^{12} + 3x^3 - x[/tex]

Answer :

To write the polynomial in descending order, we need to organize the terms based on the powers of [tex]\(x\)[/tex], starting from the highest to the lowest power. Let's go through the steps:

1. Identify the powers of [tex]\(x\)[/tex] in each term:

- [tex]\(4x^{12}\)[/tex] has a power of 12.
- [tex]\(9x^7\)[/tex] has a power of 7.
- [tex]\(3x^3\)[/tex] has a power of 3.
- [tex]\(-x\)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex], so it has a power of 1.

2. List the terms in order of their powers from highest to lowest:

- The highest power is 12, which corresponds to the term [tex]\(4x^{12}\)[/tex].
- The next highest power is 7, which corresponds to the term [tex]\(9x^7\)[/tex].
- After that, we have the power of 3, corresponding to the term [tex]\(3x^3\)[/tex].
- Finally, we have the power of 1, corresponding to the term [tex]\(-x\)[/tex].

3. Write the polynomial with the terms in descending order:

So, the polynomial in descending order is:

[tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]

4. Select the correct choice that matches this order:

The choice that corresponds to this order is:

A. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]

Thus, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches choice A.