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Answer :
To write the given polynomial in descending order, you need to arrange the terms starting with the highest power of [tex]\( x \)[/tex] and going down to the lowest. Let's look at each term of the polynomial:
The original polynomial is:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
1. Identify the degree of each term:
- [tex]\( 2x^{10} \)[/tex] has a degree of 10.
- [tex]\( 8x^6 \)[/tex] has a degree of 6.
- [tex]\( 4x^2 \)[/tex] has a degree of 2.
- [tex]\( -x \)[/tex] (which is [tex]\( -1x^1 \)[/tex]) has a degree of 1.
- [tex]\( 3 \)[/tex] is a constant, so it has a degree of 0.
2. Arrange the terms in order from the highest degree to the lowest degree:
- Start with [tex]\( 2x^{10} \)[/tex] because it has the highest degree.
- Next, use [tex]\( 8x^6 \)[/tex].
- Then, [tex]\( 4x^2 \)[/tex].
- After that, [tex]\( -x \)[/tex].
- Finally, the constant term, [tex]\( 3 \)[/tex].
3. Putting them all together, the polynomial in descending order of degrees becomes:
[tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]
After rearranging, we can see that the correct answer is:
C. [tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
This way, you have your polynomial arranged correctly from the highest power to the lowest.
The original polynomial is:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
1. Identify the degree of each term:
- [tex]\( 2x^{10} \)[/tex] has a degree of 10.
- [tex]\( 8x^6 \)[/tex] has a degree of 6.
- [tex]\( 4x^2 \)[/tex] has a degree of 2.
- [tex]\( -x \)[/tex] (which is [tex]\( -1x^1 \)[/tex]) has a degree of 1.
- [tex]\( 3 \)[/tex] is a constant, so it has a degree of 0.
2. Arrange the terms in order from the highest degree to the lowest degree:
- Start with [tex]\( 2x^{10} \)[/tex] because it has the highest degree.
- Next, use [tex]\( 8x^6 \)[/tex].
- Then, [tex]\( 4x^2 \)[/tex].
- After that, [tex]\( -x \)[/tex].
- Finally, the constant term, [tex]\( 3 \)[/tex].
3. Putting them all together, the polynomial in descending order of degrees becomes:
[tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]
After rearranging, we can see that the correct answer is:
C. [tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
This way, you have your polynomial arranged correctly from the highest power to the lowest.
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