4. Suppose n is a positive odd integer. Prove that f(x) = (x – 1)(x – 2) . .· (x – n) – 1 is irreducible in Q[x). (Hint. Assume the contrary and first reduce it to the case where f(x) = g(x)h(x) for...

Extracted text: 4. Suppose n is a positive odd integer. Prove that f(x) = (x – 1)(x – 2) . .· (x – n) – 1 is irreducible in Q[x). (Hint. Assume the contrary and first reduce it to the case where f(x) = g(x)h(x) for some non-constant integer polynomials g(x) and h(x). Then consider f(i) for integer i in [1, n], and think about g(x)² – 1 and h(x)² – 1.)