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Wikipedia has this enigmatic sentence on the page for the fundamental theorem of algebra:

...its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.

While it sounds plausible, it begs the question:

Question: In which time period did the title "fundamental theorem of algebra" get assigned to this theorem? And who were the main contributors to this title?

Searching MathSciNet for "fundamental theorem of algebra" revealed:

Bôcher, Maxime; Gauss's third proof of the fundamental theorem of algebra. Bull. Amer. Math. Soc. 1 (1895), no. 8, 205–209, MR1557382.

And by a Google Scholar search, I found this article, which mentions it in passing:

William E. Story, A New Method in Analytic Geometry, Amer. J. Math. 9, (1886), pp. 38-44.

However, it seems unlikely that these are the earliest references.

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I was going to add (reference-request) to this question, but I'm not absolutely sure it's appropriate. Anyone else have an opinion? – Ben Millwood Sep 10 '12 at 12:11
Gauss himself called (an extension of) the fundamental theorem of algebra Grundlehrsatz der Theorie der algebraischen Gleichungen in 1849. – t.b. Sep 10 '12 at 12:12
@BenMillwood: I would have said it was definitely appropriate! – user1729 Sep 10 '12 at 12:15
Fair enough. Also, if I was feeling super pedantic I might take issue with the questioner's use of "begs the question". – Ben Millwood Sep 10 '12 at 12:39

Try these references:

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As a further reference on the fundamental theorem of algebra and its history I'd recommend Remmert's contribution in chapter 4 of Numbers (Ebbinghaus et al.). – t.b. Sep 10 '12 at 12:29
Thanks for that. The Gilian paper indeed quotes Boyer "...which Gauss later referred to as the fundamental theorem of algebra...". (The book is in the library at Monash, so I'll be able to take a look tomorrow.) – Douglas S. Stones Sep 10 '12 at 12:48
@DouglasS.Stones, Boyer's book is freely available at – lhf Sep 10 '12 at 12:54

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