Answer :
Let's put the given polynomial [tex]\(4x^2 - x + 8x^6 + 3 + 2x^{10}\)[/tex] in descending order of the exponents of [tex]\(x\)[/tex].
First, identify the terms and their respective exponents:
- The term [tex]\(4x^2\)[/tex] has an exponent of 2.
- The term [tex]\(-x\)[/tex] can be interpreted as [tex]\(-1x^1\)[/tex], with an exponent of 1.
- The term [tex]\(8x^6\)[/tex] has an exponent of 6.
- The term [tex]\(3\)[/tex] can be interpreted as [tex]\(3x^0\)[/tex], with an exponent of 0.
- The term [tex]\(2x^{10}\)[/tex] has an exponent of 10.
To write the polynomial in descending order, we organize the terms by their exponents, starting with the highest:
1. The term with the highest exponent is [tex]\(2x^{10}\)[/tex].
2. The next highest exponent is 8 from the term [tex]\(8x^6\)[/tex].
3. The next is 4 from the term [tex]\(4x^2\)[/tex].
4. The next is -1 from the term [tex]\(-x\)[/tex], where [tex]\(x\)[/tex] has an exponent of 1.
5. The constant term [tex]\(3\)[/tex], where the exponent of [tex]\(x\)[/tex] is 0.
So in descending order, the polynomial should be organized as:
[tex]\[2x^{10} + 8x^6 + 4x^2 - x + 3\][/tex]
Now, let's check the options provided:
A. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
B. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
C. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
Comparing each option with our organized polynomial:
- Option A matches exactly with [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
- Option B starts with [tex]\(8x^6\)[/tex] rather than [tex]\(2x^{10}\)[/tex].
- Option C does not maintain the correct descending order.
Therefore, the correct answer is:
A. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
First, identify the terms and their respective exponents:
- The term [tex]\(4x^2\)[/tex] has an exponent of 2.
- The term [tex]\(-x\)[/tex] can be interpreted as [tex]\(-1x^1\)[/tex], with an exponent of 1.
- The term [tex]\(8x^6\)[/tex] has an exponent of 6.
- The term [tex]\(3\)[/tex] can be interpreted as [tex]\(3x^0\)[/tex], with an exponent of 0.
- The term [tex]\(2x^{10}\)[/tex] has an exponent of 10.
To write the polynomial in descending order, we organize the terms by their exponents, starting with the highest:
1. The term with the highest exponent is [tex]\(2x^{10}\)[/tex].
2. The next highest exponent is 8 from the term [tex]\(8x^6\)[/tex].
3. The next is 4 from the term [tex]\(4x^2\)[/tex].
4. The next is -1 from the term [tex]\(-x\)[/tex], where [tex]\(x\)[/tex] has an exponent of 1.
5. The constant term [tex]\(3\)[/tex], where the exponent of [tex]\(x\)[/tex] is 0.
So in descending order, the polynomial should be organized as:
[tex]\[2x^{10} + 8x^6 + 4x^2 - x + 3\][/tex]
Now, let's check the options provided:
A. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
B. [tex]\(8x^6 + 4x^2 + 3 + 2x^{10} - x\)[/tex]
C. [tex]\(2x^{10} + 4x^2 - x + 3 + 8x^6\)[/tex]
Comparing each option with our organized polynomial:
- Option A matches exactly with [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex].
- Option B starts with [tex]\(8x^6\)[/tex] rather than [tex]\(2x^{10}\)[/tex].
- Option C does not maintain the correct descending order.
Therefore, the correct answer is:
A. [tex]\(2x^{10} + 8x^6 + 4x^2 - x + 3\)[/tex]
