Which expression is not a polynomial in x because it has x in the denominator?

Correct answer: (x^2 + 1)/x

The defining condition for a polynomial in x is that, after simplification, every power of x must be a non-negative integer. In option C, division by x gives (x^2 + 1)/x = x + 1/x = x + x^(-1). The exponent -1 is negative, so the expression is not a polynomial in x. Options A and B have only permitted powers: 2 and 0 in A, and 3 and 1 in B. In option D, x^0 equals 1, so the expression becomes 7 + 4x, which is a polynomial of degree 1. A numerical fraction in a coefficient would be acceptable; the problem here is specifically that the variable x occurs in the denominator. Thus C is correct.