Question

is 4+1/x is polynomial or not

Answer 1

A rational function can be written as the quotient of two polynomials. In your example, the numerator is the polynomial 1 (constants are polynomials), and the denominator is the variable x (variables are polynomials). Another example is x 2 – 3 x + 2 x 4 + 1 . ... Here power of x is -1 hence it is not a polynomial.