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Representation of a degree 4 polynomial

Source: Tuymaada 2013, Day 2, Problem 5 Seniors

July 23, 2013
algebrapolynomialquadraticslinear algebramatrixparameterizationalgebra proposed

Problem Statement

Prove that every polynomial of fourth degree can be represented in the form P(Q(x))+R(S(x))P(Q(x))+R(S(x)), where P,Q,R,SP,Q,R,S are quadratic trinomials.
A. Golovanov
EDIT. It is confirmed that assuming the coefficients to be real, while solving the problem, earned a maximum score.
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