Recently, Hajdu and S ́ark ̈ozy studied the multiplicative decom- positions of polynomial sequences. In particular, they showed that when k ≥ 3, each infinite subset of {xk +1 : x ∈ N} is multiplicatively irreducible. In this talk, I will discuss an effective version of their result via a connection between this problem and the bipartite generalization of the well-studied Diophantine tuples.