You're given a ring $R$ and are asked to show it's not a UFD. Where do you begin? One standard trick is to apply the Rational Roots Theorem. In its most general statement, one of the theorem's hypotheses is that your ring is a UFD. So, by way of contradiction, apply the theorem and see what you get!
Welcome! Math3ma is a math blog maintained by Tai-Danae, a PhD student at the CUNY Graduate Center.