Consider a polynomial of one variable over C:
p(x)=a0+a1x+⋯+anxn,ai∈C.
We know from the Fundamental Theorem of Algebra that there exists c,αi∈C such that
p(x)=c(x−α1)⋯(x−αn),
i.e. we can factor p in linear terms.
Now, what about polynomials p(x,y) in two variables?
Is it still true that we can factor p(x,y) in linear terms? I.e. can we always write
p(x,y)=c(α1x+β1y+γ1)⋯(αnx+βny+γn)
for some c,αi,βi,γi∈C?
No comments:
Post a Comment