On the study of the decomposition of matrix polynomials into factors

We present a survey of studies of questions on the decomposition of matrix polynomials into factors. The main attention is devoted to results obtained by P. S. Kazimirs 'kii on a method of solving the problem of determining the regular factors of a matrix polynomial over an algebraically closed field of characteristic zero. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.