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]

To write the given polynomial in descending order, we need to arrange the terms starting with the highest power of [tex]$ x $[/tex] and move to the lowest power. The given polynomial is:

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

Let's organize the terms step by step:

1. Identify the powers of [tex]$ x $[/tex] in each term:
- [tex]$ 2x^{10} $[/tex] has the highest power, which is 10.
- [tex]$ 8x^6 $[/tex] has the next highest power of 6.
- [tex]$ 4x^2 $[/tex] is next with a power of 2.
- [tex]$ -x $[/tex] has a power of 1.
- [tex]$ 3 $[/tex] is a constant term with a power of 0 (technically, it's like [tex]$ 3x^0 $[/tex]).

2. Arrange the terms in descending order based on the powers of [tex]$ x $[/tex]:
- Start with the highest power: [tex]$ 2x^{10} $[/tex]
- Then, [tex]$ 8x^6 $[/tex]
- Followed by, [tex]$ 4x^2 $[/tex]
- Next, [tex]$ -x $[/tex]
- Finally, the constant term: [tex]$ 3 $[/tex]

Combining these terms, the polynomial in descending order is:

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

This matches option C. Therefore, the correct answer is:

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

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 :

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