Ordered Polynomials

A polynomial is considered an ordered polynomial with respect to a given variable when its terms are arranged so that the exponents of that variable appear in either ascending or descending order from left to right.

For example, the following polynomial is ordered with respect to x because the powers of x decrease from left to right:

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

The next polynomial is ordered with respect to x - again in descending powers - but not with respect to y:

$$ yx^5 + y^2x^3 - yx $$

This final example is ordered with respect to both x and y, with powers of each variable decreasing consistently:

$$ y^3x^4 + y^2x^2 - yx $$

And so on.