Question

Is `x^2+3x^{\frac{1}{2}}` a polynomial?

Answer 1

No.

Explanation:

`x^2+3x^{\frac{1}{2}}=x^2+3sqrtx`

Definition of a Polynomial:

1) 2 or more terms
2) No division by any variable
3) Exponents can only be natural numbers (0, 1, 2...)
4) Finite number of terms

This expression fails rule #3 so it is not a polynomial.