x^4+7x^3+14x^2+7x+x
=x^4+x+7x^3+14x^2+7x
=x(x^2-x+1)(x+1)+7x(x+1)^2
=(x+1)(x^3-x^2+x+7x^2+7x)
=x(x+1)(x^2-6x+8)
=x(x+1)(x-2)(x-4)