Question 55
Let $n$ be a positive integer. Show that the polynomial
$$
P(x, y) = x^n + x y + y^n
$$
can not be written in the form
$$
P(x, y) = G(x, y) \cdot H(x, y),
$$
where $G(x, y)$ and $H(x, y)$ are non-constant polynomials with real coefficients.
$$
P(x, y) = x^n + x y + y^n
$$
can not be written in the form
$$
P(x, y) = G(x, y) \cdot H(x, y),
$$
where $G(x, y)$ and $H(x, y)$ are non-constant polynomials with real coefficients.