The following two theorems are due to Capelli.THEOREM 1. Let g(x) and h(x) be polynomials over a field R of characteristic 0; let f(x) = g(h(x)). Then f(x) is irreducible over R if and only if(i)g(x) is irreducible over Rand(ii)h(x) - β is irreducible over R(β), where β is a root of g(x).