x8+x+1=x8+x7+x6-x7-x6-x5+x5+x4+x3-x4-x3-x2+x2+x+1
=x6(x2+x+1)-x5(x2+x+1)+x3(x2+x+1)-x2(x2+x+1)+(x2+x+1)
=(x2+x+1)(x6-x5+x3-x2+1)
x8 + x + 1 = x8 - x2 + x2 + x + 1
= ( x8 - x2 ) + ( x2 + x + 1 )
= x2 . ( x6 - 1 ) + ( x2 + x + 1 )
= x2 . ( x3 - 1 ) . ( x3 + 1 ) + ( x2 + x + 1 )
= x2 . ( x - 1 ) . ( x2 + x + 1 ) . ( x3 + 1 ) + ( x2 + x + 1 )
= ( x2 + x + 1 ) . [ x2 . ( x - 1 ) . ( x3 + 1 ) + 1 ]
= ( x2 + x + 1 ) . ( x6 + x3 - x5 - x2 + 1 )
= ( x2 + x + 1 ) . ( x6 - x5 + x3 - x2 + 1 )
