Final answer:
The function h(x)=(x²+5)/(x²+x-30) is not a polynomial because it is a ratio of two polynomials, which classifies it as a rational function.
Step-by-step explanation:
To classify the given function h(x)=(x²+5)/(x²+x-30), we need to understand what a polynomial is. A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial function is a function that can be written in the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a non-negative integer and the coefficients a0, a1 ..., an are constants.
Looking at h(x), we see that it is a ratio of two polynomials, which is known as a rational function, not a polynomial function, since polynomials do not involve division by a variable expression. So, h(x) is not a polynomial.