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Answer :
Sure, let's arrange the polynomial in descending order based on the exponents of [tex]\(x\)[/tex]. The original polynomial given is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To reorder this, we will arrange the terms starting from the highest power of [tex]\(x\)[/tex] to the lowest:
1. Identify the highest power of [tex]\(x\)[/tex], which is [tex]\(x^{11}\)[/tex]. The term is [tex]\(3x^{11}\)[/tex].
2. The next highest power is [tex]\(x^7\)[/tex]. The term is [tex]\(9x^7\)[/tex].
3. Next, we have [tex]\(x^3\)[/tex]. The term is [tex]\(5x^3\)[/tex].
4. Then, the term with [tex]\(x^1\)[/tex] which is [tex]\(-x\)[/tex].
5. Lastly, the constant term, which is [tex]\(4\)[/tex].
Putting these terms together in descending order, we get:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
So, the polynomial written in descending order is:
Option D: [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To reorder this, we will arrange the terms starting from the highest power of [tex]\(x\)[/tex] to the lowest:
1. Identify the highest power of [tex]\(x\)[/tex], which is [tex]\(x^{11}\)[/tex]. The term is [tex]\(3x^{11}\)[/tex].
2. The next highest power is [tex]\(x^7\)[/tex]. The term is [tex]\(9x^7\)[/tex].
3. Next, we have [tex]\(x^3\)[/tex]. The term is [tex]\(5x^3\)[/tex].
4. Then, the term with [tex]\(x^1\)[/tex] which is [tex]\(-x\)[/tex].
5. Lastly, the constant term, which is [tex]\(4\)[/tex].
Putting these terms together in descending order, we get:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
So, the polynomial written in descending order is:
Option D: [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
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