Factorization of sums of polynomials (Q1862253)

Given monic polynomials (real or complex) \(A\) and \(B\) of the same degree. We seek the information about the factorization of the polynomial \(C=A+B\), under some information about the factorization of \(A\) and \(B\). The inverse problem is considered as well: given the polynomial \(C\), find polynomials \(A\) and \(B\) with prescribed factorization. \vskip 1mm Many interesting examples of \(A\) and \(B\) (with different properties) are presented. The connection with problems from number theory is indicated. It seem that \textit{M. Marden}'s book: ``The geometry of the zeros of a polynomial in a complex variable'' (1949; Zbl 0038.15303) should be cited as well in the references.