x^4+7x^3+8x^2+7x+1
=x^4+x^3+x^2+6x^3+6x^2+6x+x^2+x+1
=x^2(x^2+x+1)+6x(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)(x^2+6x+1)