Answer :
To write the polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order, you need to arrange the terms from the highest exponent to the lowest. Let's break it down step-by-step:
1. Identify the Terms and Their Exponents:
- [tex]\(5x^3\)[/tex] (exponent: 3)
- [tex]\(-x\)[/tex] (which is equivalent to [tex]\(-1x^1\)[/tex], exponent: 1)
- [tex]\(9x^7\)[/tex] (exponent: 7)
- [tex]\(4\)[/tex] (constant term, exponent: 0)
- [tex]\(3x^{11}\)[/tex] (exponent: 11)
2. Order the Terms by Exponents:
- The largest exponent is 11, so [tex]\(3x^{11}\)[/tex] comes first.
- Next is the exponent 7, so [tex]\(9x^7\)[/tex] is second.
- Then, the exponent 3, so [tex]\(5x^3\)[/tex] is third.
- Next, the exponent 1, so [tex]\(-x\)[/tex] is fourth.
- Lastly, the constant term [tex]\(4\)[/tex] (exponent 0) comes last.
3. Write the Polynomial in Descending Order:
- Putting the terms together in order of their exponents gives us:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
So, the polynomial written in descending order of the exponents is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
The correct option from the choices provided is:
A. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
1. Identify the Terms and Their Exponents:
- [tex]\(5x^3\)[/tex] (exponent: 3)
- [tex]\(-x\)[/tex] (which is equivalent to [tex]\(-1x^1\)[/tex], exponent: 1)
- [tex]\(9x^7\)[/tex] (exponent: 7)
- [tex]\(4\)[/tex] (constant term, exponent: 0)
- [tex]\(3x^{11}\)[/tex] (exponent: 11)
2. Order the Terms by Exponents:
- The largest exponent is 11, so [tex]\(3x^{11}\)[/tex] comes first.
- Next is the exponent 7, so [tex]\(9x^7\)[/tex] is second.
- Then, the exponent 3, so [tex]\(5x^3\)[/tex] is third.
- Next, the exponent 1, so [tex]\(-x\)[/tex] is fourth.
- Lastly, the constant term [tex]\(4\)[/tex] (exponent 0) comes last.
3. Write the Polynomial in Descending Order:
- Putting the terms together in order of their exponents gives us:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
So, the polynomial written in descending order of the exponents is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex].
The correct option from the choices provided is:
A. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
