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You can know if a expression is a polynomial if:

1. It doesn't have fractional exponents. 
e.g. 2x^1/2
2. It doesn't have negative exponents.
e.g. 2x^-4
3. It doesn't have a variable in its denominator.
e.g. 1/x
4. Special functions, (like logarithms, etc) and square root of variables.
e.g. √5 + 7x