Question

why should a variable have a exponent which is a whole number, to be called as polynomial? why can't the exponent be fraction like x^1/2 or negative number like x^-2?

Answer 1

Even though polynomial means “many terms”, the word has come to mean just that certain kind of expression, not any old expression with many terms. It’s the accepted terminology now, and we don’t change definitions except under the most extreme circumstances

Polynomials are defined as an expression containing more than two algebraic terms.It cannot have a non whole number exponent. It has been predefined and conventionalised. Only such algebraic expressions having whole number exponents are called polynomials by convention.