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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 by the exponent of [tex]\(x\)[/tex], starting with the highest.
Here's how you can do it step by step:
1. Identify the exponent of each term:
- [tex]\(2x^{10}\)[/tex]: exponent is 10
- [tex]\(8x^6\)[/tex]: exponent is 6
- [tex]\(4x^2\)[/tex]: exponent is 2
- [tex]\(-x\)[/tex]: exponent is 1
- [tex]\(3\)[/tex]: exponent is 0 (since it’s a constant)
2. Arrange the terms in descending order of exponents:
- Start with the term with the highest exponent: [tex]\(2x^{10}\)[/tex]
- Next is: [tex]\(8x^6\)[/tex]
- Followed by: [tex]\(4x^2\)[/tex]
- Then: [tex]\(-x\)[/tex]
- Finally, the constant term: [tex]\(3\)[/tex]
3. Write the polynomial in the correct order:
- Combine the terms: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
Looking at the options provided:
- A. [tex]\(8 x^6 + 4 x^2 + 3 + 2 x^{10} - x\)[/tex]
- B. [tex]\(2 x^{10} + 4 x^2 - x + 3 + 8 x^6\)[/tex]
- C. [tex]\(3 + 2 x^{10} + 8 x^6 + 4 x^2 - x\)[/tex]
- D. [tex]\(2 x^{10} + 8 x^6 + 4 x^2 - x + 3\)[/tex]
The correct arrangement, [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex], matches option D.
Therefore, the correct choice is D.
Here's how you can do it step by step:
1. Identify the exponent of each term:
- [tex]\(2x^{10}\)[/tex]: exponent is 10
- [tex]\(8x^6\)[/tex]: exponent is 6
- [tex]\(4x^2\)[/tex]: exponent is 2
- [tex]\(-x\)[/tex]: exponent is 1
- [tex]\(3\)[/tex]: exponent is 0 (since it’s a constant)
2. Arrange the terms in descending order of exponents:
- Start with the term with the highest exponent: [tex]\(2x^{10}\)[/tex]
- Next is: [tex]\(8x^6\)[/tex]
- Followed by: [tex]\(4x^2\)[/tex]
- Then: [tex]\(-x\)[/tex]
- Finally, the constant term: [tex]\(3\)[/tex]
3. Write the polynomial in the correct order:
- Combine the terms: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
Looking at the options provided:
- A. [tex]\(8 x^6 + 4 x^2 + 3 + 2 x^{10} - x\)[/tex]
- B. [tex]\(2 x^{10} + 4 x^2 - x + 3 + 8 x^6\)[/tex]
- C. [tex]\(3 + 2 x^{10} + 8 x^6 + 4 x^2 - x\)[/tex]
- D. [tex]\(2 x^{10} + 8 x^6 + 4 x^2 - x + 3\)[/tex]
The correct arrangement, [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex], matches option D.
Therefore, the correct choice is D.
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