Answer :
To write the polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order, we need to arrange the terms by the exponent of [tex]\(x\)[/tex] from the largest to the smallest.
Here are the steps:
1. Identify the Exponents: Look at the exponents of [tex]\(x\)[/tex] in each term. The exponents are:
- [tex]\(3x^{11}\)[/tex] has an exponent of 11.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(5x^3\)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex], so it has an exponent of 1.
- The number 4 is a constant term and can be considered as [tex]\(4x^0\)[/tex] with an exponent of 0.
2. Arrange the Terms: Order the terms from highest to lowest exponent:
- The highest exponent is 11, so [tex]\(3x^{11}\)[/tex] comes first.
- Next is the term with exponent 7, which is [tex]\(9x^7\)[/tex].
- Following that is the term with exponent 3, [tex]\(5x^3\)[/tex].
- Then, the term with exponent 1, [tex]\(-x\)[/tex].
- Finally, the constant term [tex]\(4\)[/tex] with exponent 0.
3. Write the Polynomial in Order: Combine the reordered terms:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
So, the polynomial written in descending order is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex], which corresponds to choice A:
[tex]\[ A. \ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct option is A.
Here are the steps:
1. Identify the Exponents: Look at the exponents of [tex]\(x\)[/tex] in each term. The exponents are:
- [tex]\(3x^{11}\)[/tex] has an exponent of 11.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(5x^3\)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex], so it has an exponent of 1.
- The number 4 is a constant term and can be considered as [tex]\(4x^0\)[/tex] with an exponent of 0.
2. Arrange the Terms: Order the terms from highest to lowest exponent:
- The highest exponent is 11, so [tex]\(3x^{11}\)[/tex] comes first.
- Next is the term with exponent 7, which is [tex]\(9x^7\)[/tex].
- Following that is the term with exponent 3, [tex]\(5x^3\)[/tex].
- Then, the term with exponent 1, [tex]\(-x\)[/tex].
- Finally, the constant term [tex]\(4\)[/tex] with exponent 0.
3. Write the Polynomial in Order: Combine the reordered terms:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
So, the polynomial written in descending order is [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex], which corresponds to choice A:
[tex]\[ A. \ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct option is A.
