Proposition

Show that $\mathbb{R}[x]/\ev{x^2 - 4x + 3}$ is not an integral domain.

Solution

$x - 3 + \ev{x^2 - 4x + 3}, x - 1 + \ev{x^2 - 4x + 3}$ are both nonzero elements. However, their product is $0$.