# Polynomials:

(i) Show that $\mathbb{F}(x)/(x^2 -1) \cong \mathbb{F} \times \mathbb{F}$ when $\mathbb{F}$ is any field in which $1 + 1 \neq 0$.
(ii) Show that $\mathbb{R}(x)/(x^2 + a) \cong \mathbb{C}$ if a > 0, or $\mathbb{R} \times \mathbb{R}$ if a < 0.