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

Jun 4, 2018

No.

Explanation:

${x}^{2} + 3 {x}^{\setminus \frac{1}{2}} = {x}^{2} + 3 \sqrt{x}$

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.