List the possible ways a 5-th degree polynomial f(x) can factor into a product of irreducibles over the following fields. use l1(x), l2(x), for linear polynomials q1(x), q2(x), for irreducible quadratic polynomials, c(x) for an irreducible cubic polynomial and f(x) for an irreducible quartic polynomial. in each case determine the number of zeros of f(x) in the given field. a) q. (example: f(x) = l1(x)l2(x)c(x), two zeros.) b) r. c) c.