Answer :
To write the polynomial in descending order, you need to arrange the terms based on the power of [tex]\( x \)[/tex], starting with the highest power and going to the lowest. Here's how you can do it step-by-step:
1. Identify the Terms and Their Exponents:
- [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] or [tex]\(-1x^1\)[/tex] has an exponent of 1.
2. Order the Terms by Exponent:
- First, list the terms starting with the largest exponent and end with the smallest.
- The largest exponent here is 12, followed by 7, then 3, and finally 1.
3. Re-write the Polynomial:
- Arrange the terms in the descending order of their exponents:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
4. Select the Correct Option:
- The polynomial arranged in descending order is [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
- This matches option A.
Therefore, the correct choice is A: [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
1. Identify the Terms and Their Exponents:
- [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] or [tex]\(-1x^1\)[/tex] has an exponent of 1.
2. Order the Terms by Exponent:
- First, list the terms starting with the largest exponent and end with the smallest.
- The largest exponent here is 12, followed by 7, then 3, and finally 1.
3. Re-write the Polynomial:
- Arrange the terms in the descending order of their exponents:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
4. Select the Correct Option:
- The polynomial arranged in descending order is [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
- This matches option A.
Therefore, the correct choice is A: [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex].
