Answer :
To find the correct answer, we need to rewrite the given polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order based on the exponents of [tex]\(x\)[/tex]. This means we organize the polynomial terms from the highest degree to the lowest degree:
1. Identify the term with the highest power of [tex]\(x\)[/tex], which is [tex]\(3x^{11}\)[/tex].
2. Next, find the term with the second highest power, which is [tex]\(9x^7\)[/tex].
3. The next highest is [tex]\(5x^3\)[/tex].
4. Then, the term [tex]\(-x\)[/tex] which is the same as [tex]\(-1x^1\)[/tex].
5. Lastly, we have the constant term [tex]\(4\)[/tex].
Putting these terms in order from highest degree to lowest, we get:
[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]
Thus, the correct choice is:
B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
1. Identify the term with the highest power of [tex]\(x\)[/tex], which is [tex]\(3x^{11}\)[/tex].
2. Next, find the term with the second highest power, which is [tex]\(9x^7\)[/tex].
3. The next highest is [tex]\(5x^3\)[/tex].
4. Then, the term [tex]\(-x\)[/tex] which is the same as [tex]\(-1x^1\)[/tex].
5. Lastly, we have the constant term [tex]\(4\)[/tex].
Putting these terms in order from highest degree to lowest, we get:
[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]
Thus, the correct choice is:
B. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
