a^5+a+1
=(a^5-a^2)+(a^2+a+1)
=a^2*(a^3-1)+(a^2+a+1)
=a^2(a-1)(a^2+a+1)+(a^2+a+1)
=(a^2+a+1)[a^2(a-1)+1]
=(a^2+a+1)(a^3-a^2+1)