Geodesic
A Multivariable form of the Fundamental Theorem of Algebra
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 271-272

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Let H(x) be a homogeneous polynomial in n indeterminates over an algebraically closed field K. A necesssary and sufficient condition is given for H(x) to admit a factorization of the form a, b∈ Kn, and “∘” is the usual inner product. This condition involves the linear derivatives of H(x).
DOI : 10.4153/CMB-1983-043-x
Mots-clés : 12D05, 12E05 
Salzberg, Pablo M. A Multivariable form of the Fundamental Theorem of Algebra. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 271-272. doi: 10.4153/CMB-1983-043-x
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     title = {A {Multivariable} form of the {Fundamental} {Theorem} of {Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {271--272},
     year = {1983},
     volume = {26},
     number = {3},
     doi = {10.4153/CMB-1983-043-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-043-x/}
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