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Before Cuneo's proof, all known proofs of the Fundamental Theorem of Algebra were relying on the complex numbers, evene to prove that every real polynomial can be expressed as a product of first or second order real polynomials. The involvement of the complex field forbids to precisely understand which are the essential features of the proof and what it is relying on. The new proof obtained by Cuneo doesn't involve complex numbers at all, clearly pointing out the ingredients that are essntial to reach the result. Taking advantage of this, one may wonder which are the resulting consequences on a didactic presentation of the factorization of polynomials and which is the influence implied by this result on a vision of mathematics and of its fundaments. The proposed research should reach new results capable to further enlarge the knowledge on this field, and to put into a clear prospective the ones already obtained.
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