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Answer :
To write the polynomial [tex]\( 4x^2 - x + 8x^6 + 3 + 2x^{10} \)[/tex] in descending order, we need to arrange the terms from the highest exponent to the lowest exponent.
Let’s break it down step-by-step:
1. Identify the terms and their exponents:
- [tex]\(4x^2\)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] has an exponent of 1.
- [tex]\(8x^6\)[/tex] has an exponent of 6.
- [tex]\(3\)[/tex] is a constant term with an exponent of 0.
- [tex]\(2x^{10}\)[/tex] has an exponent of 10.
2. Arrange these terms in descending order of their exponents:
- The highest exponent is 10, so we start with [tex]\(2x^{10}\)[/tex].
- Next, we have the term with exponent 6, which is [tex]\(8x^6\)[/tex].
- Following that, we have the term with exponent 2, which is [tex]\(4x^2\)[/tex].
- After that, we have the term with exponent 1, which is [tex]\(-x\)[/tex].
- Lastly, we have the constant term, which is [tex]\(3\)[/tex].
3. Combine the arranged terms to write the polynomial in descending order:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
By comparing this with the given choices:
- A. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
- B. [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
- C. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- D. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
The correct answer is option A:
[tex]\[
\boxed{2x^{10} + 8x^6 + 4x^2 - x + 3}
\][/tex]
Let’s break it down step-by-step:
1. Identify the terms and their exponents:
- [tex]\(4x^2\)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] has an exponent of 1.
- [tex]\(8x^6\)[/tex] has an exponent of 6.
- [tex]\(3\)[/tex] is a constant term with an exponent of 0.
- [tex]\(2x^{10}\)[/tex] has an exponent of 10.
2. Arrange these terms in descending order of their exponents:
- The highest exponent is 10, so we start with [tex]\(2x^{10}\)[/tex].
- Next, we have the term with exponent 6, which is [tex]\(8x^6\)[/tex].
- Following that, we have the term with exponent 2, which is [tex]\(4x^2\)[/tex].
- After that, we have the term with exponent 1, which is [tex]\(-x\)[/tex].
- Lastly, we have the constant term, which is [tex]\(3\)[/tex].
3. Combine the arranged terms to write the polynomial in descending order:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
By comparing this with the given choices:
- A. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
- B. [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
- C. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- D. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
The correct answer is option A:
[tex]\[
\boxed{2x^{10} + 8x^6 + 4x^2 - x + 3}
\][/tex]
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