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Polynomials – operations, factoring, solving equations, applications

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Polynomials are usually used in those of mathematical problems which are qualified to be inverse problems: you have some measurements showing relationship between two variables and you want to know what type of function describes this relationship. Example: restoration of distribution of stars in a star cluster. There is an integral equation called Abel's equation, showing how projected distribution of stars relates to 3D - distribution. This unknown distribution can be approximated by polynomials the coefficients of which are to be found using existing measurements for two -dimensional distribution (projection on the sky). This si a very interesting problem, but I don't know how this can help you.