Question 7
Let $n$ be a positive integer. Prove that
$$P(x,y)=x^n+xy+y^n$$
cannot be written as $P(x,y)=G(x,y)H(x,y)$, where $G,H$ are nonconstant polynomials with real coefficients.
$$P(x,y)=x^n+xy+y^n$$
cannot be written as $P(x,y)=G(x,y)H(x,y)$, where $G,H$ are nonconstant polynomials with real coefficients.