In lectures this week we were studying highest common factors (greatest common divisors) of polynomials. We went through all of the proofs, but we didn't actually do an example - and now that I've been set one, I'm a bit lost!

I found the Wikipedia page on calculating them, and there are two methods: factoring and the Euclidian algorithm. I don't think I'm supposed to use factoring - the questions set are of degree 4 / 5. So, that leaves me with the algorithm.

Found here. However, I don't understand how the example they do in that table relates to the algorithm that is specified nearer the top of the article. Would someone be able to explain it step by step, or make up another example and go through it?

Thanks guys!