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Answer :
To write the given polynomial in descending order, follow these steps:
1. Identify the terms and their exponents: The original polynomial is [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex]. Let's break this down:
- [tex]\(2x^{10}\)[/tex] (power of 10)
- [tex]\(8x^6\)[/tex] (power of 6)
- [tex]\(4x^2\)[/tex] (power of 2)
- [tex]\(-x\)[/tex] or [tex]\(-1x^1\)[/tex] (power of 1)
- [tex]\(3\)[/tex] (constant term, power of 0)
2. Order the terms by descending powers: Arrange the terms starting from the highest power of [tex]\(x\)[/tex] to the lowest:
- The highest power is [tex]\(2x^{10}\)[/tex].
- The next highest is [tex]\(8x^6\)[/tex].
- Then comes [tex]\(4x^2\)[/tex].
- After that is [tex]\(-x\)[/tex].
- Finally, the constant term [tex]\(3\)[/tex] comes last.
3. Write the polynomial in descending order:
- The polynomial in descending order becomes: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
4. Match with the given options:
- Compare the rearranged polynomial with each option provided:
- A. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- B. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
- C. [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
- D. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
- The correct match, which follows [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex], is Option D.
Therefore, the polynomial written in descending order is [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex], and the correct option is D.
1. Identify the terms and their exponents: The original polynomial is [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex]. Let's break this down:
- [tex]\(2x^{10}\)[/tex] (power of 10)
- [tex]\(8x^6\)[/tex] (power of 6)
- [tex]\(4x^2\)[/tex] (power of 2)
- [tex]\(-x\)[/tex] or [tex]\(-1x^1\)[/tex] (power of 1)
- [tex]\(3\)[/tex] (constant term, power of 0)
2. Order the terms by descending powers: Arrange the terms starting from the highest power of [tex]\(x\)[/tex] to the lowest:
- The highest power is [tex]\(2x^{10}\)[/tex].
- The next highest is [tex]\(8x^6\)[/tex].
- Then comes [tex]\(4x^2\)[/tex].
- After that is [tex]\(-x\)[/tex].
- Finally, the constant term [tex]\(3\)[/tex] comes last.
3. Write the polynomial in descending order:
- The polynomial in descending order becomes: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
4. Match with the given options:
- Compare the rearranged polynomial with each option provided:
- A. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
- B. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
- C. [tex]\(3 + 2x^{10} + 8x^6 + 4x^2 - x\)[/tex]
- D. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
- The correct match, which follows [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex], is Option D.
Therefore, the polynomial written in descending order is [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex], and the correct option is D.
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