Thursday, 28 April 2016

abstract algebra - Do polynomials in two variables always factor in linear terms?

Consider a polynomial of one variable over C:
p(x)=a0+a1x++anxn,aiC.


We know from the Fundamental Theorem of Algebra that there exists c,αiC such that
p(x)=c(xα1)(xαn),


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,γiC?


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...