What is the theory of finding roots of a polynomial equation by looking at the factors of the $a_n$ and $a_0$ term called?

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This is commonly taught in high schools in the context of factoring polynomials. I remember this method even has its own wikipedia page (with a proof) but I forget what was the theory called. Could anybody remind me of the name?

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What you are looking for is the rational roots (or zeros) theorem. I wrote this up a while back (maybe you will find it helpful):

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