The endosymbiotic theory concerns the origins of mitochondria and chloroplasts, which are organelles of eukaryotic cells. According to this theory, these originated as prokaryotic endosymbionts, which came to live inside eukaryotic cells.he theory postulates that the mitochondria evolved from aerobic bacteria (probably proteobacteria, related to the rickettsias), and that the chloroplast evolved from endosymbiotic cyanobacteria (autotrophic prokaryotes).
The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient a n = 1.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator. The importance of the partial fraction decomposition lies in the fact that it provides an algorithm for computing the antiderivative of a rational function. In symbols, one can use partial fraction expansion to change a rational fraction in the form f g {\disp