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Answer :
Sure! Let's work through arranging the terms of the polynomial in descending order.
The given polynomial is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To write the polynomial in descending order, we need to arrange the terms from the highest exponent of [tex]\( x \)[/tex] to the lowest. Let's go through the steps:
1. Identify the terms and their exponents:
- [tex]\( 3x^{11} \)[/tex] has an exponent of 11.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 5x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- [tex]\( 4 \)[/tex] is a constant term, which can be considered [tex]\(4x^0\)[/tex], with an exponent of 0.
2. Order the terms by decreasing exponent:
- Start with the term having the highest exponent, which is [tex]\( 3x^{11} \)[/tex].
- Next is [tex]\( 9x^7 \)[/tex].
- Followed by [tex]\( 5x^3 \)[/tex].
- Then comes [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]).
- Lastly, the constant term [tex]\(4\)[/tex].
3. Write the polynomial in the new order:
- The polynomial in descending order is: [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
From the options provided, the correct one is:
B. [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
I hope this helps! If you have more questions, feel free to ask.
The given polynomial is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To write the polynomial in descending order, we need to arrange the terms from the highest exponent of [tex]\( x \)[/tex] to the lowest. Let's go through the steps:
1. Identify the terms and their exponents:
- [tex]\( 3x^{11} \)[/tex] has an exponent of 11.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 5x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- [tex]\( 4 \)[/tex] is a constant term, which can be considered [tex]\(4x^0\)[/tex], with an exponent of 0.
2. Order the terms by decreasing exponent:
- Start with the term having the highest exponent, which is [tex]\( 3x^{11} \)[/tex].
- Next is [tex]\( 9x^7 \)[/tex].
- Followed by [tex]\( 5x^3 \)[/tex].
- Then comes [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]).
- Lastly, the constant term [tex]\(4\)[/tex].
3. Write the polynomial in the new order:
- The polynomial in descending order is: [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
From the options provided, the correct one is:
B. [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex]
I hope this helps! If you have more questions, feel free to ask.
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