There is an infinite number of polynomials of the form ax^2 + bx + c, where a, b, and c are rational numbers, that are factors of the polynomial x^4 - 1. Any polynomial of the form (ax^2 + bx + c) where a, b, and c are rational numbers such that ax^2 + bx + c is a factor of x^4 - 1 would satisfy the problem statement. Since there are an infinite number of rational numbers, there are an infinite number of polynomials of the given form that could potentially be factors.