A rational function is the quotient of two polynomial functions.
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A polynomial function is simply a function that is made of one or more mononomials. For example 4x^2+3x-5 A rational function is when a polynomial function is divided by another polynomial function.
Thee basic concept is that an rational function is one polynomial divided by another polynomial. The coefficients of these polynomials need not be rational numbers.
Basically, a rational expression is one that can be written as one polynomial, divided by another polynomial.
Since the question did not specify a rational polynomial, the answer is a polynomial of degree 3.
A polynomial can be factored if it has a rational root. If f(x) is a polynomial function of x and if there is a rational number p such that f(p) = 0 then f(x) = (x-p)*g(x) where g(x) is a polynomial whose order is one less than the order of f(x). If p = q/r where q and r are integers, then (x - p) = (x - q/r) = (rx - q)/r which is a rational binomial factor. This does not work if p is irrational which is why p must be rational.