A transformation of a polynomial equation which is of the form where and are polynomials and does not vanish at a root of . The cubic equation is a special case of such a transformation. Tschirnhaus (1683) showed that a polynomial of degree can be reduced to a form in which the and terms have 0 coefficients. In 1786, E. S. Bring showed that a general quintic equation can be reduced to the form
In 1834, G. B. Jerrard showed that a Tschirnhaus transformation can be used to eliminate the , , and terms for a general polynomial equation of degree .