Polynomials are expressions like $15x^3 - 14x^2 + 8$. Questions tagged with this concern common operations on polynomials, like adding, multiplying, polynomial long division, factoring and solving for roots.

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Does there exist a proof of the Abel-Ruffini theorem without using Galois theory?

Question: Does there exist a proof of the Abel-Ruffini theorem without using Galois theory? Original: Prove that there exists a polynomial $P$ with $\deg P \geq 6$ such that the minima and maxima ...