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"Non-polynomials" may be just about anything; how alike or different they are will depend on what specific restrictions you put on such functions, or whether you are even talking about functions.
In my opinion the question is poorly defined, since "non-polynomial" could be just about anything.
Descartes did not invent polynomials.
dividing polynomials is just like dividing whole nos..
Reciprocal polynomials come with a number of connections with their original polynomials