Final answer:
The expression x²+x-√5 is not considered a polynomial because it contains a term (-√5) with a fractional exponent, which is against the definition of a polynomial which allows only non-negative integral exponents.
Step-by-step explanation:
The given expression x²+x-√5 is not a polynomial. The reason is that a polynomial is an algebraic expression that consists of a sum of terms, each term including a variable raised to a non-negative integral exponent and a coefficient. In the given expression, the term -√5 includes a square root, which is equivalent to raising the variable to a fractional exponent (specifically, a 1/2 exponent), as shown by the identity x² = √x. This inclusion of a fractional exponent means that the expression does not satisfy the definition of a polynomial, where exponents must be whole numbers.