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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 arrange the polynomial terms in descending order, you should order them from the highest exponent to the lowest. The given polynomial is:

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

Let's identify the terms and their exponents:

- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x^1\)[/tex]) has an exponent of 1.

Now, arrange these terms from the highest to the lowest exponent:

1. Start with [tex]\( 4x^{12} \)[/tex] because it has the highest exponent.
2. Next is [tex]\( 9x^7 \)[/tex].
3. Then, [tex]\( 3x^3 \)[/tex].
4. Finally, [tex]\(-x\)[/tex] with the smallest exponent.

Putting them together, the polynomial written in descending order is:

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

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

So, the correct option is C.

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