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Answer :
To write the polynomial in descending order, you need to arrange the terms based on the exponents of [tex]\( x \)[/tex] from highest to lowest.
The given polynomial is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Let's organize the terms by the exponents of [tex]\( x \)[/tex]:
1. Identify the term with the highest exponent: [tex]\( 3x^{11} \)[/tex].
2. Next, find the term with the next highest exponent: [tex]\( 9x^7 \)[/tex].
3. Then, the term with the next highest exponent: [tex]\( 5x^3 \)[/tex].
4. The term with [tex]\( x^1 \)[/tex]: [tex]\(-x\)[/tex].
5. Finally, the constant term: [tex]\( 4 \)[/tex].
Arrange these in descending order of their exponents:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
The polynomial in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct choice is:
D. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
The given polynomial is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Let's organize the terms by the exponents of [tex]\( x \)[/tex]:
1. Identify the term with the highest exponent: [tex]\( 3x^{11} \)[/tex].
2. Next, find the term with the next highest exponent: [tex]\( 9x^7 \)[/tex].
3. Then, the term with the next highest exponent: [tex]\( 5x^3 \)[/tex].
4. The term with [tex]\( x^1 \)[/tex]: [tex]\(-x\)[/tex].
5. Finally, the constant term: [tex]\( 4 \)[/tex].
Arrange these in descending order of their exponents:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
The polynomial in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct choice is:
D. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
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