# What is the condition for a polynomial to be factorizable in linear real factors?

I have a polynomial $p_a(x,y)= x^2F(a)+y^2G(a)-xH(a)-I(a)$ where $F(a)$, $G(a)$, $H(a)$ and $I(a)$ some real fuctions of $a$ are. Which conditions must satisfy $a$ so that I can factorize the polynomial $p_a(x,y)$ in lineal real factors?

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Isn't it impossible to have bring out linear factors in $y$ here without having a mixed $xy$ term? – Alexander Gruber Jan 4 '13 at 22:18
I fear you are right – Pablo Elias Jan 7 '13 at 10:31