x^5 +x +1 = x^5 - x^2 + x^2 +x +1 = x^2 (x^3 -1 ) +(x^2 +x +1) =x^2 (x-1)(x^2 +x +1) + (x^2 +x +1) =(x^2 +x +1) (x^3 -x^2 +1 )
