A polynomial is a sum of terms, each of which is the product of a constant and some constellation of variables to integer non-negative powers. Anything with a variable in a denominator, a non-linear function such as absolute value, or square root (a fractional power) will <em>not</em> be a polynomial.
The constants in a polynomial may be rational or irrational. The polynomials we generally study are ones with real coefficients, but there is no reason why the coefficients could not be complex numbers.