(x^2+3x+1)(x^2+4x+1)x^4+7x^3+14x^2+7x+1=x^2*(x^2+7x+14+7/x+1/x^2)=x^2[(x+1/x)^2+7*(x+1/x)+12]=x^2(x+1/x+3)(x+1/x+4)=[x*(x+1/x+3)][x*(x+1/x+4)]=(x^2+3x+1)(x^2+4x+1)