Hello I am a little bit confused about something. I have a question:

Find the solutions of

and use Hensel's Lemma to solve .

But I'm a bit confused, i can use the roots of the first equation and use hensel's lemma to get ALL the roots? I used it and got 2 (90, and 199 solve the 2nd equation) , but is not a field, so might there not be extra roots of due to the lack of unique factorisation?

Thanks for any help