For arbitrary non-constant polynomials $f_1(x),\ldots,f_{2018}(x)\in\mathbb Z[x]$, is it always possible to find a polynomial $g(x)\in\mathbb Z[x]$ such that $$f_1(g(x)),\ldots,f_{2018}(g(x))$$are all reducible.
Source: IMOC 2018 A2
Tags: polynomial, algebra, irreducibility
For arbitrary non-constant polynomials $f_1(x),\ldots,f_{2018}(x)\in\mathbb Z[x]$, is it always possible to find a polynomial $g(x)\in\mathbb Z[x]$ such that $$f_1(g(x)),\ldots,f_{2018}(g(x))$$are all reducible.