Irreducibility criterion for certain trinomials

In this article we study the irreducibility of polynomials of the form $x^n+{ϵ}_1{x}^m+p^k{ϵ}_2$, $p$ being a prime number. We will show that they are irreducible for $m=1$. We have also provided the cyclotomic factors and reducibility criterion for trinomials of the form $x^n+{ϵ}_1{x}^m+{ϵ}_2$, where ${ϵ}_i\in \{-1,+1\}$. This corrects few of the existing results of W. Ljuggren’s on $x^n+{ϵ}_1{x}^m+{ϵ}_2$.