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

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Answer 1 · 2018-06-04T16:57:47

No.

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

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.

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