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

Answer 1

To list the powers of the given polynomials in descending order, we need to identify the terms in each polynomial based on their degrees.

1. For the first polynomial:
\(3x^4 - x^3 + 4x^5 - 2x^2 + 1\)

The terms arranged in descending order of their powers (degrees) would be:
- \(4x^5\) (degree 5)
- \(3x^4\) (degree 4)
- \(-x^3\) (degree 3)
- \(-2x^2\) (degree 2)
- \(1\) (degree 0)

So, the first polynomial in descending order is:
\(4x^5 + 3x^4 - x^3 - 2x^2 + 1\)

2. For the second polynomial:
\(4x^5 + 3x^4 - x^3 - 2x^2 + 1\)

This is already presented in descending order:
- \(4x^5\) (degree 5)
- \(3x^4\) (degree 4)
- \(-x^3\) (degree 3)
- \(-2x^2\) (degree 2)
- \(1\) (degree 0)

In conclusion, both polynomials are listed in descending order of their powers, and they are as follows:

1. \(4x^5 + 3x^4 - x^3 - 2x^2 + 1\) (from the first polynomial after rearranging).
2. \(4x^5 + 3x^4 - x^3 - 2x^2 + 1\) (already in order from the second polynomial).

So, both polynomials are equal after ordering and both have the same terms.