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Answer :
To write a polynomial in descending order, we arrange the terms from the one with the highest exponent (largest power) to the one with the lowest exponent. Let's go through the steps for the given polynomial:
The original polynomial is:
[tex]\( 4x^2 - x + 8x^6 + 3 + 2x^{10} \)[/tex]
Now, we'll identify each term and its exponent:
1. [tex]\( 4x^2 \)[/tex] has an exponent of 2.
2. [tex]\(-x\)[/tex] can be considered as [tex]\(-1x^1\)[/tex], with an exponent of 1.
3. [tex]\( 8x^6 \)[/tex] has an exponent of 6.
4. [tex]\( 3 \)[/tex] can be considered as [tex]\( 3x^0\)[/tex], with an exponent of 0 since there is no [tex]\(x\)[/tex].
5. [tex]\( 2x^{10} \)[/tex] has an exponent of 10.
Next, arrange these terms in order of descending exponent (from highest to lowest):
1. Start with [tex]\(2x^{10}\)[/tex] because it has the highest exponent of 10.
2. Then [tex]\(8x^6\)[/tex] since it has the next highest exponent of 6.
3. Next comes [tex]\(4x^2\)[/tex] with an exponent of 2.
4. Then [tex]\(-x\)[/tex] as it has an exponent of 1.
5. Finally, [tex]\(3\)[/tex] with the exponent of 0.
Arranging them in this order, we get:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
Therefore, the polynomial written in descending order is:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
The correct answer is:
A. [tex]\( 2x^{10}+8x^6+4x^2-x+3 \)[/tex]
The original polynomial is:
[tex]\( 4x^2 - x + 8x^6 + 3 + 2x^{10} \)[/tex]
Now, we'll identify each term and its exponent:
1. [tex]\( 4x^2 \)[/tex] has an exponent of 2.
2. [tex]\(-x\)[/tex] can be considered as [tex]\(-1x^1\)[/tex], with an exponent of 1.
3. [tex]\( 8x^6 \)[/tex] has an exponent of 6.
4. [tex]\( 3 \)[/tex] can be considered as [tex]\( 3x^0\)[/tex], with an exponent of 0 since there is no [tex]\(x\)[/tex].
5. [tex]\( 2x^{10} \)[/tex] has an exponent of 10.
Next, arrange these terms in order of descending exponent (from highest to lowest):
1. Start with [tex]\(2x^{10}\)[/tex] because it has the highest exponent of 10.
2. Then [tex]\(8x^6\)[/tex] since it has the next highest exponent of 6.
3. Next comes [tex]\(4x^2\)[/tex] with an exponent of 2.
4. Then [tex]\(-x\)[/tex] as it has an exponent of 1.
5. Finally, [tex]\(3\)[/tex] with the exponent of 0.
Arranging them in this order, we get:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
Therefore, the polynomial written in descending order is:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
The correct answer is:
A. [tex]\( 2x^{10}+8x^6+4x^2-x+3 \)[/tex]
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