Question

Which lists the powers in descending order?

3x^4-x^3+4x^5-2x^2+1
4x^5+3x^4-x^3-2x^2+1
1-2x^2-x^3+4x^5+3x^4
4x^5-2x^2-x^3+3x^4+1

Answer 1

To list the powers of \( x \) in descending order for each polynomial, we will identify the term with the highest power and order them accordingly.

1. **First Polynomial**: \( 3x^4 - x^3 + 4x^5 - 2x^2 + 1 \)
- Highest power: \( 4x^5 \)
- Ordered: \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)

2. **Second Polynomial**: \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)
- Highest power: \( 4x^5 \)
- Already in order: \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)

3. **Third Polynomial**: \( 1 - 2x^2 - x^3 + 4x^5 + 3x^4 \)
- Highest power: \( 4x^5 \)
- Ordered: \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)

4. **Fourth Polynomial**: \( 4x^5 - 2x^2 - x^3 + 3x^4 + 1 \)
- Highest power: \( 4x^5 \)
- Ordered: \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)

Now we can summarize the orders of powers in descending order:

1. \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)
2. \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)
3. \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)
4. \( 4x^5 + 3x^4 - x^3 - 2x^2 + 1 \)

All the listed polynomials have the same descending order of powers when sorted correctly.