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Answer :
To rewrite the given polynomial in descending order, we need to order the terms by decreasing exponents of [tex]\(x\)[/tex]. Let's break down the given polynomial:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
Here's how to rearrange the terms:
1. Identify the exponents:
- [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] is equivalent to [tex]\(-1x^1\)[/tex], so its exponent is 1
- [tex]\(3\)[/tex] has an exponent of 0 (because it's a constant term)
2. Order the terms from highest to lowest exponent:
- The term with the highest exponent is [tex]\(2x^{10}\)[/tex].
- Next comes [tex]\(8x^6\)[/tex].
- Then [tex]\(4x^2\)[/tex].
- After that is [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]).
- Finally, the constant [tex]\(3\)[/tex].
3. Rewrite the polynomial in descending order:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
Now let's see which of the provided options matches our reordered polynomial:
- Option A: [tex]\(2 x^{10}+4 x^2-x+3+8 x^6\)[/tex]
- Option B: [tex]\(2 x^{10}+8 x^6+4 x^2-x+3\)[/tex]
- Option C: [tex]\(3+2 x^{10}+8 x^6+4 x^2-x\)[/tex]
- Option D: [tex]\(8 x^6+4 x^2+3+2 x^{10}-x\)[/tex]
The correct order is found in Option B: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
So, the polynomial written in descending order is correctly represented by Option B.
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
Here's how to rearrange the terms:
1. Identify the exponents:
- [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] is equivalent to [tex]\(-1x^1\)[/tex], so its exponent is 1
- [tex]\(3\)[/tex] has an exponent of 0 (because it's a constant term)
2. Order the terms from highest to lowest exponent:
- The term with the highest exponent is [tex]\(2x^{10}\)[/tex].
- Next comes [tex]\(8x^6\)[/tex].
- Then [tex]\(4x^2\)[/tex].
- After that is [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]).
- Finally, the constant [tex]\(3\)[/tex].
3. Rewrite the polynomial in descending order:
[tex]\[
2x^{10} + 8x^6 + 4x^2 - x + 3
\][/tex]
Now let's see which of the provided options matches our reordered polynomial:
- Option A: [tex]\(2 x^{10}+4 x^2-x+3+8 x^6\)[/tex]
- Option B: [tex]\(2 x^{10}+8 x^6+4 x^2-x+3\)[/tex]
- Option C: [tex]\(3+2 x^{10}+8 x^6+4 x^2-x\)[/tex]
- Option D: [tex]\(8 x^6+4 x^2+3+2 x^{10}-x\)[/tex]
The correct order is found in Option B: [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
So, the polynomial written in descending order is correctly represented by Option B.
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