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Answer :
To write the given polynomial in descending order, we should arrange the terms from the highest power of [tex]\( x \)[/tex] to the lowest power. Here's how you can do it step-by-step:
1. Identify the Terms and Their Degrees:
Let's look at each term in the polynomial [tex]\( 3x^3 + 9x^7 - x + 4x^{12} \)[/tex]:
- [tex]\( 3x^3 \)[/tex] has a degree of 3.
- [tex]\( 9x^7 \)[/tex] has a degree of 7.
- [tex]\( -x \)[/tex] can be written as [tex]\(-1x^1\)[/tex], which has a degree of 1.
- [tex]\( 4x^{12} \)[/tex] has a degree of 12.
2. Order the Terms by Degree:
We need to arrange these terms by descending order of their degrees. The order from highest to lowest degree will be:
- [tex]\( 4x^{12} \)[/tex] (degree 12)
- [tex]\( 9x^7 \)[/tex] (degree 7)
- [tex]\( 3x^3 \)[/tex] (degree 3)
- [tex]\( -x \)[/tex] (degree 1)
3. Write the Polynomial in Descending Order:
After arranging the terms by degree, the polynomial is:
[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 A. So, the correct answer is:
A. [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
1. Identify the Terms and Their Degrees:
Let's look at each term in the polynomial [tex]\( 3x^3 + 9x^7 - x + 4x^{12} \)[/tex]:
- [tex]\( 3x^3 \)[/tex] has a degree of 3.
- [tex]\( 9x^7 \)[/tex] has a degree of 7.
- [tex]\( -x \)[/tex] can be written as [tex]\(-1x^1\)[/tex], which has a degree of 1.
- [tex]\( 4x^{12} \)[/tex] has a degree of 12.
2. Order the Terms by Degree:
We need to arrange these terms by descending order of their degrees. The order from highest to lowest degree will be:
- [tex]\( 4x^{12} \)[/tex] (degree 12)
- [tex]\( 9x^7 \)[/tex] (degree 7)
- [tex]\( 3x^3 \)[/tex] (degree 3)
- [tex]\( -x \)[/tex] (degree 1)
3. Write the Polynomial in Descending Order:
After arranging the terms by degree, the polynomial is:
[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 A. So, the correct answer is:
A. [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
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