Answer :
To write the polynomial in descending order, we need to arrange the terms according to the exponents of [tex]\(x\)[/tex], starting with the highest and going to the lowest. Let's look step by step at the polynomial given:
The original polynomial is:
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]
1. Identify the exponents:
- The term [tex]\(3x^{10}\)[/tex] has the highest exponent, which is 10.
- The next highest exponent is 6 from the term [tex]\(x^6\)[/tex].
- Then, the term [tex]\(2x^2\)[/tex] has an exponent of 2.
- The linear term [tex]\(-4x\)[/tex] has an exponent of 1.
- The constant term [tex]\(8\)[/tex] can be thought to have an exponent of 0 (since [tex]\(x^0 = 1\)[/tex]).
2. Arrange the terms in descending order of exponents:
- Start with the term with the highest exponent: [tex]\(3x^{10}\)[/tex]
- Next is the term with the highest remaining exponent: [tex]\(x^6\)[/tex]
- Follow with the next highest: [tex]\(2x^2\)[/tex]
- Next is [tex]\(-4x\)[/tex]
- Finally, the constant term comes last: [tex]\(8\)[/tex]
3. Write out the polynomial in descending order:
[tex]\[
3x^{10} + x^6 + 2x^2 - 4x + 8
\][/tex]
Now let's match this with the given options:
A. [tex]\(8 + 3x^{10} + x^6 + 2x^2 - 4x\)[/tex]
B. [tex]\(3x^{10} + 2x^2 - 4x + 8 + x^6\)[/tex]
C. [tex]\(x^6 + 2x^2 + 8 + 3x^{10} - 4x\)[/tex]
D. [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex]
The correct answer, where the polynomial is arranged in descending order, is:
[tex]\[ D. \, 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
So the answer is Option D.
The original polynomial is:
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]
1. Identify the exponents:
- The term [tex]\(3x^{10}\)[/tex] has the highest exponent, which is 10.
- The next highest exponent is 6 from the term [tex]\(x^6\)[/tex].
- Then, the term [tex]\(2x^2\)[/tex] has an exponent of 2.
- The linear term [tex]\(-4x\)[/tex] has an exponent of 1.
- The constant term [tex]\(8\)[/tex] can be thought to have an exponent of 0 (since [tex]\(x^0 = 1\)[/tex]).
2. Arrange the terms in descending order of exponents:
- Start with the term with the highest exponent: [tex]\(3x^{10}\)[/tex]
- Next is the term with the highest remaining exponent: [tex]\(x^6\)[/tex]
- Follow with the next highest: [tex]\(2x^2\)[/tex]
- Next is [tex]\(-4x\)[/tex]
- Finally, the constant term comes last: [tex]\(8\)[/tex]
3. Write out the polynomial in descending order:
[tex]\[
3x^{10} + x^6 + 2x^2 - 4x + 8
\][/tex]
Now let's match this with the given options:
A. [tex]\(8 + 3x^{10} + x^6 + 2x^2 - 4x\)[/tex]
B. [tex]\(3x^{10} + 2x^2 - 4x + 8 + x^6\)[/tex]
C. [tex]\(x^6 + 2x^2 + 8 + 3x^{10} - 4x\)[/tex]
D. [tex]\(3x^{10} + x^6 + 2x^2 - 4x + 8\)[/tex]
The correct answer, where the polynomial is arranged in descending order, is:
[tex]\[ D. \, 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
So the answer is Option D.
