Examples of expressions that are not polynomials include ( \frac{1}{x} ), ( \sqrt{x} ), and ( e^x ). A rational function like ( \frac{x^2 + 1}{x - 2} ) is also not a polynomial because it has a denominator that is a variable expression. Additionally, expressions with negative or fractional exponents, such as ( x^{-1} ) or ( x^{1/2} ), are not polynomials.
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