What can a translation of a polynomial do to bring the equation into a nicer form?

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I'm very sorry if this is a stupid question, but I'm very stressed and would appreciate any advice at all!

I'm trying to write a report (on radicals) and one of the questions I'm being asked just isn't clicking in my brain and I was really hoping someone could reword it maybe, or point me in the right direction of any online resources!

My exam question is:

"There is a general principle of applying a transformation (generally a translation $y=x-e$ to bring the equation into a nicer form. What can that translation achieve for an equation of higher degree (depressed form)? "

I don't know if I'm being stupid, but I don't quite understand what's being asked. I'm unsure of the specific importance on the translation $y=x-e$. Is this a commonly used translation to simplify polynomials? Because I just thought that moved the mapping to the right slightly?

I have looked everywhere and came up short so anything at all would be so so appreciated!

(and please be nice I'm one stressy breakdown from never recovering lol)