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Answer :
Sure! Let's arrange the given polynomial in descending order, step by step.
The polynomial you have is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To write a polynomial in descending order, you need to arrange the terms starting with the highest power of [tex]\( x \)[/tex] and go towards the lowest. Here's how you can do it:
1. Identify the term with the highest power of [tex]\( x \)[/tex]. In this polynomial, it's [tex]\( 3x^{11} \)[/tex] since 11 is the largest exponent.
2. The next highest power is [tex]\( x^7 \)[/tex], so [tex]\( 9x^7 \)[/tex] is the second term.
3. After that, look for [tex]\( x^3 \)[/tex], which gives you [tex]\( 5x^3 \)[/tex].
4. The term [tex]\(-x\)[/tex] corresponds to [tex]\( x^1 \)[/tex].
5. Finally, the constant term [tex]\( 4 \)[/tex] is written last, as it has no variable part.
Putting it all together, the polynomial in descending order by the powers of [tex]\( x \)[/tex] is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Now, let's match this with the options:
- A. [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex] ✔️
- B. [tex]\( 3x^{11} + 9x^7 - x + 4 + 5x^3 \)[/tex]
- C. [tex]\( 9x^7 + 5x^3 + 4 + 3x^{11} - x \)[/tex]
- D. [tex]\( 4 + 3x^{11} + 9x^7 + 5x^3 - x \)[/tex]
The correct answer, where the polynomial is correctly arranged in descending order, is Option A: [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex].
The polynomial you have is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
To write a polynomial in descending order, you need to arrange the terms starting with the highest power of [tex]\( x \)[/tex] and go towards the lowest. Here's how you can do it:
1. Identify the term with the highest power of [tex]\( x \)[/tex]. In this polynomial, it's [tex]\( 3x^{11} \)[/tex] since 11 is the largest exponent.
2. The next highest power is [tex]\( x^7 \)[/tex], so [tex]\( 9x^7 \)[/tex] is the second term.
3. After that, look for [tex]\( x^3 \)[/tex], which gives you [tex]\( 5x^3 \)[/tex].
4. The term [tex]\(-x\)[/tex] corresponds to [tex]\( x^1 \)[/tex].
5. Finally, the constant term [tex]\( 4 \)[/tex] is written last, as it has no variable part.
Putting it all together, the polynomial in descending order by the powers of [tex]\( x \)[/tex] is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Now, let's match this with the options:
- A. [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex] ✔️
- B. [tex]\( 3x^{11} + 9x^7 - x + 4 + 5x^3 \)[/tex]
- C. [tex]\( 9x^7 + 5x^3 + 4 + 3x^{11} - x \)[/tex]
- D. [tex]\( 4 + 3x^{11} + 9x^7 + 5x^3 - x \)[/tex]
The correct answer, where the polynomial is correctly arranged in descending order, is Option A: [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex].
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