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Polynomial is an algebraic expression where each term is a constant, a variable or a product of a variable in which the variable has a whole number exponent. Non Polynomial is: the exponent of a variable is not a whole number, and the variable is in the denominator.
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To differentiate polynomials from non-polynomials, polynomials have the following conditions:

1)  NO fractional / rational exponents in variables.

     Example:  3x^{ \frac{1}{2} } + 4x + 7
2)  NO variable as denominator in simplified form
     Example:   \frac{5}{x-6}

3)  NO radical expression in simplified form
     Example:   \sqrt{x^{3} } + 6

4)  NO negative exponents.

     Example:  -5x⁻⁵ + 2
5)  A constant is a polynomial.  It is called constant polynomial.
     Example:  -25    polynomial

Non polynomial:
All that is not polynomial.
1) It may have a radical expression is simplified form.
2)  It may have a variable as denominator is simplified form.
3)  The variables may have negative or rational/fractional exponents.

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