Question

Is it possible to divide one polynomial into another and your answer is not a polynomial? Please provide an example and an explanation.

Answer 1

One of the requirements of a polynomial is that all of the terms of the expression have non-negative exponents.
If you divide a polynomial by another polynomial with higher exponents, then the result will be an expression containing negative exponents; this result would not be a polynomial.

A simple example of this would be x^3 / x^4; the result of this would be x^(-1). Although x^3 and x^4 both qualify as polynomials, the result x^(-1) would not be a polynomial, because it contains a variable with a negative exponent.

Answer 2

Thank you so much!

Answer 3

No problem! Going to sleep now :)