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Answer :
To write a polynomial in descending order, we need to arrange its terms based on the exponents of the variable [tex]\( x \)[/tex], from highest to lowest. Let's analyze the given polynomial:
The original polynomial is:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
Follow these steps to arrange it in descending order:
1. Identify the Terms and Their Exponents:
- [tex]\( 2x^{10} \)[/tex] has the highest exponent, which is 10.
- [tex]\( 8x^6 \)[/tex] has the next highest exponent, which is 6.
- [tex]\( 4x^2 \)[/tex] has an exponent of 2.
- [tex]\( -x \)[/tex] is the same as [tex]\(-1x^1\)[/tex], so the exponent is 1.
- The constant term [tex]\( 3 \)[/tex] doesn't have a variable, which means it technically has an exponent of 0.
2. Arrange the Terms:
- Start with the term having the highest exponent: [tex]\( 2x^{10} \)[/tex].
- Follow with the next highest: [tex]\( 8x^6 \)[/tex].
- Next, come the terms with lower exponents in order: [tex]\( 4x^2 \)[/tex], [tex]\(-x\)[/tex], and lastly, the constant term [tex]\( 3 \)[/tex].
Putting it all together, the polynomial arranged in descending order by the exponents is:
[tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]
The correct answer that matches this order is option D:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
The original polynomial is:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
Follow these steps to arrange it in descending order:
1. Identify the Terms and Their Exponents:
- [tex]\( 2x^{10} \)[/tex] has the highest exponent, which is 10.
- [tex]\( 8x^6 \)[/tex] has the next highest exponent, which is 6.
- [tex]\( 4x^2 \)[/tex] has an exponent of 2.
- [tex]\( -x \)[/tex] is the same as [tex]\(-1x^1\)[/tex], so the exponent is 1.
- The constant term [tex]\( 3 \)[/tex] doesn't have a variable, which means it technically has an exponent of 0.
2. Arrange the Terms:
- Start with the term having the highest exponent: [tex]\( 2x^{10} \)[/tex].
- Follow with the next highest: [tex]\( 8x^6 \)[/tex].
- Next, come the terms with lower exponents in order: [tex]\( 4x^2 \)[/tex], [tex]\(-x\)[/tex], and lastly, the constant term [tex]\( 3 \)[/tex].
Putting it all together, the polynomial arranged in descending order by the exponents is:
[tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]
The correct answer that matches this order is option D:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
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