Performing Lin´s method via Routh-type algorithms or Hurwitz-type determinants

Lin´s method for finding a quadratic factor of a polynomial is too well known. Basically it is to perform long divisions on the polynomial in question by a quadratic factor shown in the last three terms of the polynomial or in the remainder. The new approach is to use Routh-Hurwitz type algorithms or determinants to evaluate the factor iteratively.