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Answer :
To arrange a polynomial in descending order, we need to order all the terms from the highest to the lowest exponent of [tex]\( x \)[/tex]. Let's look at the polynomial given:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Here are the steps to ordering it:
1. Identify the exponents of each term:
- [tex]\( 3x^{11} \)[/tex] has the highest exponent, which is 11.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 5x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- The constant term [tex]\( 4 \)[/tex] can be considered as [tex]\( 4x^0 \)[/tex] with an exponent of 0.
2. Reorder the terms from highest to lowest exponent:
- Start with the term with the highest exponent: [tex]\( 3x^{11} \)[/tex].
- Next is the term with the next highest exponent: [tex]\( 9x^7 \)[/tex].
- Followed by: [tex]\( 5x^3 \)[/tex].
- Then: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\( 4 \)[/tex].
3. Write the polynomial in descending order:
- Combine all these ordered terms to get:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Thus, the polynomial written in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
So, the correct answer is option B:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Here are the steps to ordering it:
1. Identify the exponents of each term:
- [tex]\( 3x^{11} \)[/tex] has the highest exponent, which is 11.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 5x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- The constant term [tex]\( 4 \)[/tex] can be considered as [tex]\( 4x^0 \)[/tex] with an exponent of 0.
2. Reorder the terms from highest to lowest exponent:
- Start with the term with the highest exponent: [tex]\( 3x^{11} \)[/tex].
- Next is the term with the next highest exponent: [tex]\( 9x^7 \)[/tex].
- Followed by: [tex]\( 5x^3 \)[/tex].
- Then: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\( 4 \)[/tex].
3. Write the polynomial in descending order:
- Combine all these ordered terms to get:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Thus, the polynomial written in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
So, the correct answer is option B:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
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