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Answer :
To write the polynomial in descending order, you need to arrange the terms based on the powers of [tex]\( x \)[/tex], starting from the highest to the lowest power. Here's how you can do it:
1. Look at the given polynomial:
[tex]\[
5x^3 - x + 9x^7 + 4 + 3x^{11}
\][/tex]
2. Identify the powers of [tex]\( x \)[/tex] in each term:
- [tex]\( 3x^{11} \)[/tex] has the highest power, which is 11.
- [tex]\( 9x^7 \)[/tex] has a power of 7.
- [tex]\( 5x^3 \)[/tex] has a power of 3.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has a power of 1.
- The constant [tex]\(4\)[/tex] can be thought of as [tex]\(4x^0\)[/tex] and has a power of 0.
3. Arrange these terms in order of descending powers:
- Start with the term with power 11: [tex]\(3x^{11}\)[/tex]
- Next, the term with power 7: [tex]\(9x^7\)[/tex]
- Then, the term with power 3: [tex]\(5x^3\)[/tex]
- After that, the term with power 1: [tex]\(-x\)[/tex]
- Finally, the constant term: [tex]\(4\)[/tex]
4. Write the polynomial in descending order:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
Therefore, the polynomial written in descending order is:
[tex]\[ \boxed{3x^{11} + 9x^7 + 5x^3 - x + 4} \][/tex]
This corresponds to option B, which is the correct answer.
1. Look at the given polynomial:
[tex]\[
5x^3 - x + 9x^7 + 4 + 3x^{11}
\][/tex]
2. Identify the powers of [tex]\( x \)[/tex] in each term:
- [tex]\( 3x^{11} \)[/tex] has the highest power, which is 11.
- [tex]\( 9x^7 \)[/tex] has a power of 7.
- [tex]\( 5x^3 \)[/tex] has a power of 3.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has a power of 1.
- The constant [tex]\(4\)[/tex] can be thought of as [tex]\(4x^0\)[/tex] and has a power of 0.
3. Arrange these terms in order of descending powers:
- Start with the term with power 11: [tex]\(3x^{11}\)[/tex]
- Next, the term with power 7: [tex]\(9x^7\)[/tex]
- Then, the term with power 3: [tex]\(5x^3\)[/tex]
- After that, the term with power 1: [tex]\(-x\)[/tex]
- Finally, the constant term: [tex]\(4\)[/tex]
4. Write the polynomial in descending order:
[tex]\[
3x^{11} + 9x^7 + 5x^3 - x + 4
\][/tex]
Therefore, the polynomial written in descending order is:
[tex]\[ \boxed{3x^{11} + 9x^7 + 5x^3 - x + 4} \][/tex]
This corresponds to option B, which is the correct answer.
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