Show that {x^{2}, x^{2}+x+1, x^{2}+x, x-1} is LD

I took like 20 mins to find the solution with trial and error to get

(x^{2}+x) - 1/2(x^{2}+x+1) -1/2(x-1) -1/2(x^{2}) =0 ---> LD

Are there any formula or shortcut for this?

How about {x^{4}+x^{2}+1, x^{4}-x^{2}+1, x^{4}-x^{2}-1}?