Answer :
To solve this problem, we need to arrange the terms of the polynomial [tex]\( 3x^3 + 9x^7 - x + 4x^{12} \)[/tex] in descending order based on the power of [tex]\( x \)[/tex]. Let's do this step-by-step:
1. Identify the terms and their corresponding powers:
- [tex]\( 3x^3 \)[/tex] has a power of 3.
- [tex]\( 9x^7 \)[/tex] has a power of 7.
- [tex]\( -x \)[/tex] (or equivalently, [tex]\( -1x^1 \)[/tex]) has a power of 1.
- [tex]\( 4x^{12} \)[/tex] has a power of 12.
2. Arrange these terms in descending order from the highest power to the lowest power:
- The highest power here is 12, so we place [tex]\( 4x^{12} \)[/tex] first.
- The next highest power is 7, so [tex]\( 9x^7 \)[/tex] comes next.
- Following that, the next highest power is 3, so [tex]\( 3x^3 \)[/tex] is placed after [tex]\( 9x^7 \)[/tex].
- Finally, the term with the lowest power (1) is [tex]\( -x \)[/tex].
3. Combining these terms, we obtain the polynomial in descending order as:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
Thus, the polynomial in descending order is [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
Therefore, the correct option is:
[tex]\[
\boxed{D. \, 4x^{12} + 9x^7 + 3x^3 - x}
\][/tex]
1. Identify the terms and their corresponding powers:
- [tex]\( 3x^3 \)[/tex] has a power of 3.
- [tex]\( 9x^7 \)[/tex] has a power of 7.
- [tex]\( -x \)[/tex] (or equivalently, [tex]\( -1x^1 \)[/tex]) has a power of 1.
- [tex]\( 4x^{12} \)[/tex] has a power of 12.
2. Arrange these terms in descending order from the highest power to the lowest power:
- The highest power here is 12, so we place [tex]\( 4x^{12} \)[/tex] first.
- The next highest power is 7, so [tex]\( 9x^7 \)[/tex] comes next.
- Following that, the next highest power is 3, so [tex]\( 3x^3 \)[/tex] is placed after [tex]\( 9x^7 \)[/tex].
- Finally, the term with the lowest power (1) is [tex]\( -x \)[/tex].
3. Combining these terms, we obtain the polynomial in descending order as:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
Thus, the polynomial in descending order is [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
Therefore, the correct option is:
[tex]\[
\boxed{D. \, 4x^{12} + 9x^7 + 3x^3 - x}
\][/tex]
