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