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

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

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

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

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

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

Answer :

To write a polynomial in descending order, you arrange the terms from the highest degree to the lowest degree. Here's how you can do that for the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex]:

1. Identify the degrees of each term:
- [tex]\(4x^{12}\)[/tex] has a degree of 12.
- [tex]\(9x^7\)[/tex] has a degree of 7.
- [tex]\(3x^3\)[/tex] has a degree of 3.
- [tex]\(-x\)[/tex] has a degree of 1.

2. Order the terms by descending power:
Start with the term that has the highest degree and proceed to the lowest.

3. Re-order the polynomial:
Begin with [tex]\(4x^{12}\)[/tex] as it has the highest degree, followed by [tex]\(9x^7\)[/tex], then [tex]\(3x^3\)[/tex], and finally [tex]\(-x\)[/tex].

Putting it all together, the polynomial in descending order is:

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

Therefore, the correct choice is:

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

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