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Answer :
To write a polynomial in descending order, we order the terms from the one with the highest power of [tex]\( x \)[/tex] to the lowest. Let's look at the polynomial provided:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Here are the steps to arrange it in descending order:
1. Identify the terms: The polynomial has four terms: [tex]\( 3x^3 \)[/tex], [tex]\( 9x^7 \)[/tex], [tex]\(-x\)[/tex], and [tex]\( 4x^{12} \)[/tex].
2. Identify the exponent of each term:
- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], so it has an exponent of 1.
3. Arrange the terms by descending exponent values:
- The highest exponent is 12, so [tex]\( 4x^{12} \)[/tex] comes first.
- Next is the exponent 7, so [tex]\( 9x^7 \)[/tex] comes second.
- Then the exponent 3, so [tex]\( 3x^3 \)[/tex] comes third.
- Finally, the exponent 1, so [tex]\(-x\)[/tex] comes last.
4. Write the polynomial in descending order:
- Combine these: [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
Therefore, the polynomial written in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
This matches option D from the provided choices.
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Here are the steps to arrange it in descending order:
1. Identify the terms: The polynomial has four terms: [tex]\( 3x^3 \)[/tex], [tex]\( 9x^7 \)[/tex], [tex]\(-x\)[/tex], and [tex]\( 4x^{12} \)[/tex].
2. Identify the exponent of each term:
- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], so it has an exponent of 1.
3. Arrange the terms by descending exponent values:
- The highest exponent is 12, so [tex]\( 4x^{12} \)[/tex] comes first.
- Next is the exponent 7, so [tex]\( 9x^7 \)[/tex] comes second.
- Then the exponent 3, so [tex]\( 3x^3 \)[/tex] comes third.
- Finally, the exponent 1, so [tex]\(-x\)[/tex] comes last.
4. Write the polynomial in descending order:
- Combine these: [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
Therefore, the polynomial written in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
This matches option D from the provided choices.
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