Question 91
Let $f(x)$ be the polynomial with integer coefficients ($f(x)$ is not constant) such that
$$
(x^3 + 4x^2 + 4x + 3)f(x) = (x^3 - 2x^2 + 2x - 1)f(x + 1).
$$
Prove that for each positive integer $n$ ($n \ge 8$), $f(n)$ has at least five distinct prime divisors.
$$
(x^3 + 4x^2 + 4x + 3)f(x) = (x^3 - 2x^2 + 2x - 1)f(x + 1).
$$
Prove that for each positive integer $n$ ($n \ge 8$), $f(n)$ has at least five distinct prime divisors.