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Answer :
We start with the polynomial
[tex]$$5x^3 - x + 9x^7 + 4 + 3x^{11}.$$[/tex]
Our goal is to rewrite it in descending order, which means arranging the terms so that the exponents decrease from left to right.
1. Identify the exponents of the terms:
- The term [tex]$3x^{11}$[/tex] has an exponent of 11.
- The term [tex]$9x^7$[/tex] has an exponent of 7.
- The term [tex]$5x^3$[/tex] has an exponent of 3.
- The term [tex]$-x$[/tex] has an exponent of 1.
- The constant [tex]$4$[/tex] has an exponent of 0.
2. Arrange the terms from the highest exponent to the lowest:
- First, the term with exponent 11: [tex]$3x^{11}$[/tex].
- Next, the term with exponent 7: [tex]$9x^7$[/tex].
- Then, the term with exponent 3: [tex]$5x^3$[/tex].
- Followed by the term with exponent 1: [tex]$-x$[/tex].
- Finally, the constant term: [tex]$4$[/tex].
3. Write the polynomial in the new order:
[tex]$$3x^{11} + 9x^{7} + 5x^{3} - x + 4.$$[/tex]
Among the options provided, this matches option C.
Thus, the correct answer is option C.
[tex]$$5x^3 - x + 9x^7 + 4 + 3x^{11}.$$[/tex]
Our goal is to rewrite it in descending order, which means arranging the terms so that the exponents decrease from left to right.
1. Identify the exponents of the terms:
- The term [tex]$3x^{11}$[/tex] has an exponent of 11.
- The term [tex]$9x^7$[/tex] has an exponent of 7.
- The term [tex]$5x^3$[/tex] has an exponent of 3.
- The term [tex]$-x$[/tex] has an exponent of 1.
- The constant [tex]$4$[/tex] has an exponent of 0.
2. Arrange the terms from the highest exponent to the lowest:
- First, the term with exponent 11: [tex]$3x^{11}$[/tex].
- Next, the term with exponent 7: [tex]$9x^7$[/tex].
- Then, the term with exponent 3: [tex]$5x^3$[/tex].
- Followed by the term with exponent 1: [tex]$-x$[/tex].
- Finally, the constant term: [tex]$4$[/tex].
3. Write the polynomial in the new order:
[tex]$$3x^{11} + 9x^{7} + 5x^{3} - x + 4.$$[/tex]
Among the options provided, this matches option C.
Thus, the correct answer is option C.
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