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Answer :
To write the polynomial [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex] in descending order, you must organize the terms from the highest exponent to the lowest exponent. Here’s how you can do it:
1. Identify the exponents: Look at each term and its exponent:
- [tex]\(2x^{10}\)[/tex] has an exponent of 10.
- [tex]\(8x^6\)[/tex] has an exponent of 6.
- [tex]\(4x^2\)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x^1\)[/tex]) has an exponent of 1.
- [tex]\(3\)[/tex] doesn't have a variable, so consider it as [tex]\(3x^0\)[/tex] with an exponent of 0.
2. Order the terms by exponents: Arrange the terms from the highest exponent to the lowest:
- The highest exponent is 10, so the first term is [tex]\(2x^{10}\)[/tex].
- The next highest exponent is 6, so the next term is [tex]\(8x^6\)[/tex].
- The next highest exponent is 2, so [tex]\(4x^2\)[/tex] comes next.
- Followed by [tex]\(-x\)[/tex] which has an exponent of 1.
- Finally, [tex]\(3\)[/tex] with an exponent of 0.
3. Write the polynomial: After arranging the terms, the polynomial written in descending order is:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
Looking at the given options, option C matches this arrangement:
- C. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
Therefore, the correct answer is C.
1. Identify the exponents: Look at each term and its exponent:
- [tex]\(2x^{10}\)[/tex] has an exponent of 10.
- [tex]\(8x^6\)[/tex] has an exponent of 6.
- [tex]\(4x^2\)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] (which is the same as [tex]\(-1x^1\)[/tex]) has an exponent of 1.
- [tex]\(3\)[/tex] doesn't have a variable, so consider it as [tex]\(3x^0\)[/tex] with an exponent of 0.
2. Order the terms by exponents: Arrange the terms from the highest exponent to the lowest:
- The highest exponent is 10, so the first term is [tex]\(2x^{10}\)[/tex].
- The next highest exponent is 6, so the next term is [tex]\(8x^6\)[/tex].
- The next highest exponent is 2, so [tex]\(4x^2\)[/tex] comes next.
- Followed by [tex]\(-x\)[/tex] which has an exponent of 1.
- Finally, [tex]\(3\)[/tex] with an exponent of 0.
3. Write the polynomial: After arranging the terms, the polynomial written in descending order is:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
Looking at the given options, option C matches this arrangement:
- C. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
Therefore, the correct answer is C.
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