Answer :
Sure, let's solve the problem step-by-step.
Question: Which of the following shows the polynomial below written in descending order?
Given polynomial:
[tex]\[ x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To write the polynomial in descending order, we need to arrange the terms by the power of [tex]\(x\)[/tex] in decreasing order.
1. Identify the term with the highest power of [tex]\(x\)[/tex]:
- [tex]\(3x^{11}\)[/tex] (highest power, 11)
2. Next, find the term with the next highest power of [tex]\(x\)[/tex]:
- [tex]\(9x^7\)[/tex] (next highest power, 7)
3. Then, look for the term with the next highest power of [tex]\(x\)[/tex]:
- [tex]\(x^3\)[/tex] (next highest power, 3)
4. The linear term:
- [tex]\(-x\)[/tex] (x has power 1)
5. Lastly, the constant term:
- [tex]\(4\)[/tex] (constant term, no [tex]\(x\)[/tex])
Arrange these terms in descending order of their exponents:
[tex]\[ 3x^{11} + 9x^7 + x^3 - x + 4 \][/tex]
Now, let's compare this arranged polynomial with the given options:
A. [tex]\(3x^{11} + 9x^7 - x + 4 + 5\)[/tex]
- This is incorrect because the terms are not all present, and an extraneous "+ 5" is included.
B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
- This is incorrect because the term [tex]\(x^3\)[/tex] should not have a coefficient of 5.
C. [tex]\(4 + 3x^{11} + 9x^7 + 5x^3 - x\)[/tex]
- This is incorrect because the terms are not in descending order.
D. [tex]\(9x^7 + 5x^3 + 4 + 3x^{11} - x\)[/tex]
- This is incorrect because [tex]\(3x^{11}\)[/tex] should come first, and the coefficient for [tex]\(x^3\)[/tex] is incorrect and should not precede [tex]\(x^3\)[/tex] or be 5.
The correct answer is:
[tex]\[ 3x^{11} + 9x^7 + x^3 - x + 4 \][/tex]
So the correct choice is:
B. [tex]\(3x^{11} + 9x^7 + x^3 - x + 4\)[/tex]
Question: Which of the following shows the polynomial below written in descending order?
Given polynomial:
[tex]\[ x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To write the polynomial in descending order, we need to arrange the terms by the power of [tex]\(x\)[/tex] in decreasing order.
1. Identify the term with the highest power of [tex]\(x\)[/tex]:
- [tex]\(3x^{11}\)[/tex] (highest power, 11)
2. Next, find the term with the next highest power of [tex]\(x\)[/tex]:
- [tex]\(9x^7\)[/tex] (next highest power, 7)
3. Then, look for the term with the next highest power of [tex]\(x\)[/tex]:
- [tex]\(x^3\)[/tex] (next highest power, 3)
4. The linear term:
- [tex]\(-x\)[/tex] (x has power 1)
5. Lastly, the constant term:
- [tex]\(4\)[/tex] (constant term, no [tex]\(x\)[/tex])
Arrange these terms in descending order of their exponents:
[tex]\[ 3x^{11} + 9x^7 + x^3 - x + 4 \][/tex]
Now, let's compare this arranged polynomial with the given options:
A. [tex]\(3x^{11} + 9x^7 - x + 4 + 5\)[/tex]
- This is incorrect because the terms are not all present, and an extraneous "+ 5" is included.
B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
- This is incorrect because the term [tex]\(x^3\)[/tex] should not have a coefficient of 5.
C. [tex]\(4 + 3x^{11} + 9x^7 + 5x^3 - x\)[/tex]
- This is incorrect because the terms are not in descending order.
D. [tex]\(9x^7 + 5x^3 + 4 + 3x^{11} - x\)[/tex]
- This is incorrect because [tex]\(3x^{11}\)[/tex] should come first, and the coefficient for [tex]\(x^3\)[/tex] is incorrect and should not precede [tex]\(x^3\)[/tex] or be 5.
The correct answer is:
[tex]\[ 3x^{11} + 9x^7 + x^3 - x + 4 \][/tex]
So the correct choice is:
B. [tex]\(3x^{11} + 9x^7 + x^3 - x + 4\)[/tex]
