On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

We provide an alternative exposition of a result due to Schinzel. Fix an integer $k\ge 2$. For almost all choices of positive integers $n_1<\cdots <n_k$, we show that the polynomial $F(x)=1+x^{n_1}+\cdots +x^{n_k}$, removed of its cyclotomic factors, is irreducible.