x*x+x+1=0
(x-1)(x*x+x+1)=0
x^3-1=0
x^3=1
x^7+2x^6+x^5+x^4+x^3+x*x+1
=x^6*x+2x^6+x^3*x^2+x^3*x+x^3+x*x+1
=x+2+x*x+x+1+x^2+1
=2x^2+2x+4
=2(x^2+x+1)+2
=2*0+2
=2