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Answer :
To arrange the polynomial in descending order, we need to order the terms by the power of [tex]\( x \)[/tex], starting from the highest power to the lowest power.
The given polynomial is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Let's follow these steps to rewrite it in descending order:
1. Identify the powers of [tex]\(x\)[/tex] for each term:
- [tex]\( 4x^{12} \)[/tex] has the exponent 12.
- [tex]\( 9x^7 \)[/tex] has the exponent 7.
- [tex]\( 3x^3 \)[/tex] has the exponent 3.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has the exponent 1.
2. Order the terms from highest to lowest power:
- First, write the term with the highest power: [tex]\( 4x^{12} \)[/tex].
- Next, write the term with the next highest power: [tex]\( 9x^7 \)[/tex].
- Then, write the term with the next highest power: [tex]\( 3x^3 \)[/tex].
- Finally, write the term with the lowest power: [tex]\(-x\)[/tex].
3. The polynomial in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
So, the answer is B: [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
The given polynomial is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Let's follow these steps to rewrite it in descending order:
1. Identify the powers of [tex]\(x\)[/tex] for each term:
- [tex]\( 4x^{12} \)[/tex] has the exponent 12.
- [tex]\( 9x^7 \)[/tex] has the exponent 7.
- [tex]\( 3x^3 \)[/tex] has the exponent 3.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has the exponent 1.
2. Order the terms from highest to lowest power:
- First, write the term with the highest power: [tex]\( 4x^{12} \)[/tex].
- Next, write the term with the next highest power: [tex]\( 9x^7 \)[/tex].
- Then, write the term with the next highest power: [tex]\( 3x^3 \)[/tex].
- Finally, write the term with the lowest power: [tex]\(-x\)[/tex].
3. The polynomial in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
So, the answer is B: [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
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