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Answer :
Sure, let's organize the polynomial in the correct order:
The given polynomial is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
To write a polynomial in descending order, you need to arrange the terms starting from the highest power (exponent) of [tex]\(x\)[/tex] to the lowest.
Here's how you do it:
1. Identify the exponents: Look at each term and note the power of [tex]\(x\)[/tex].
- [tex]\(3x^3\)[/tex] has an exponent of 3.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], so it has an exponent of 1.
- [tex]\(4x^{12}\)[/tex] has an exponent of 12.
2. Arrange in descending order: Now, sort these terms based on the exponent from the highest to the lowest:
- Highest to lowest powers are [tex]\(12\)[/tex], [tex]\(7\)[/tex], [tex]\(3\)[/tex], and [tex]\(1\)[/tex].
3. Write the polynomial in descending order:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Therefore, the polynomial in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
This matches option C.
So, the correct answer is C.
The given polynomial is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
To write a polynomial in descending order, you need to arrange the terms starting from the highest power (exponent) of [tex]\(x\)[/tex] to the lowest.
Here's how you do it:
1. Identify the exponents: Look at each term and note the power of [tex]\(x\)[/tex].
- [tex]\(3x^3\)[/tex] has an exponent of 3.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], so it has an exponent of 1.
- [tex]\(4x^{12}\)[/tex] has an exponent of 12.
2. Arrange in descending order: Now, sort these terms based on the exponent from the highest to the lowest:
- Highest to lowest powers are [tex]\(12\)[/tex], [tex]\(7\)[/tex], [tex]\(3\)[/tex], and [tex]\(1\)[/tex].
3. Write the polynomial in descending order:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Therefore, the polynomial in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
This matches option C.
So, the correct answer is C.
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