Can a polynomial have a fraction as an exponent?

No, a polynomial cannot have a fraction as an exponent on its variable terms.

Understanding Polynomials

A polynomial is a specific type of algebraic expression. To qualify as a polynomial, an expression must adhere to certain rules regarding its exponents and variables.

Key Characteristics of Polynomials

• No Variables Inside Radicals: A polynomial cannot have a variable under a radical sign (e.g., √x).
• No Negative Exponents: The exponent of any variable term must be a non-negative integer.
• No Fractional Exponents: A polynomial cannot contain fractional exponents on its variable terms. According to the provided reference: "For an algebraic expression to be a polynomial, It must not have a variable inside the radical symbol. It must have no negative exponents. No fractional exponents in the variable."

Examples

• Polynomial: 3x² + 2x + 1 (Exponents are non-negative integers)
• Not a Polynomial: 4x^1/2 + x - 5 (Contains a fractional exponent: 1/2)
• Not a Polynomial: 2x^-1 + 5 (Contains a negative exponent: -1)
• Not a Polynomial: √x + 7 (Contains a variable inside a radical)

In summary, the exponents on variables in a polynomial must be whole numbers (0, 1, 2, 3,...). Fractional exponents are not allowed.