Contest problem without using heavy machinery in number theory
Note that $f(x) = (x^2 + x - 2)^2 + x^2$, and use the fact that if a prime $p = 4k + 3$ divides $a^2 + b^2$ then $p$ divides both $a$ and $b$.
Note that $f(x) = (x^2 + x - 2)^2 + x^2$, and use the fact that if a prime $p = 4k + 3$ divides $a^2 + b^2$ then $p$ divides both $a$ and $b$.