Basically, i am doing some cryptography, i need to show that a polynomial i have, which is not irreducibale, implies it is not primitive. I am having trouble factorising these rather large polynomials. I have checked to see whether the following polynomials are irreducible and found there factorisation with maple. Could someone please teach me how you would do these by hand. x5+x+1=(x2+x+1)(x3-x2+1) Another example: x5+x4+1=(x2+x+1)(x3-x+1) an explanation of either would be gratefuly appreciated, thank you.