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Answer :
To rearrange the polynomial in descending order, we need to list the terms starting with the highest power of [tex]\( x \)[/tex] and ending with the constant term. Here's the given polynomial:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Let's break down the steps to write this in descending order:
1. Identify the powers of [tex]\( x \)[/tex] in each term:
- [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.
- [tex]\( 9x^7 \)[/tex] has a power of 7.
- [tex]\( 4 \)[/tex] is a constant term and can be considered as [tex]\( 4x^0 \)[/tex].
- [tex]\( 3x^{11} \)[/tex] has a power of 11.
2. Order the terms from highest to lowest power:
- The highest power is [tex]\( x^{11} \)[/tex]. The term is [tex]\( 3x^{11} \)[/tex].
- Next is [tex]\( x^7 \)[/tex]. The term is [tex]\( 9x^7 \)[/tex].
- Then, [tex]\( x^3 \)[/tex]. The term is [tex]\( 5x^3 \)[/tex].
- Then, [tex]\( x^1 \)[/tex]. The term is [tex]\( -x \)[/tex].
- Finally, the constant term [tex]\( 4 \)[/tex].
3. Write the polynomial:
So, ordered from the highest power to the lowest, the polynomial becomes:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
This matches option C:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct answer is option C.
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Let's break down the steps to write this in descending order:
1. Identify the powers of [tex]\( x \)[/tex] in each term:
- [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.
- [tex]\( 9x^7 \)[/tex] has a power of 7.
- [tex]\( 4 \)[/tex] is a constant term and can be considered as [tex]\( 4x^0 \)[/tex].
- [tex]\( 3x^{11} \)[/tex] has a power of 11.
2. Order the terms from highest to lowest power:
- The highest power is [tex]\( x^{11} \)[/tex]. The term is [tex]\( 3x^{11} \)[/tex].
- Next is [tex]\( x^7 \)[/tex]. The term is [tex]\( 9x^7 \)[/tex].
- Then, [tex]\( x^3 \)[/tex]. The term is [tex]\( 5x^3 \)[/tex].
- Then, [tex]\( x^1 \)[/tex]. The term is [tex]\( -x \)[/tex].
- Finally, the constant term [tex]\( 4 \)[/tex].
3. Write the polynomial:
So, ordered from the highest power to the lowest, the polynomial becomes:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
This matches option C:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Therefore, the correct answer is option C.
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