Linear algebra| finding a base

First of all, sorry if my English or any of the terms that I used are incorrect, I am learning math in a different language than english.

So after not being able to study for the past two months I started going over Linear algebra again and need some help to get back in.

I am stuck on this question: Given the following:

V = R4[x] (that's supposed to be a small 4 on the bottom for 4)

dim U = 3

Looking at the sub-space "U": U={$p(-1)=p^n(-1)=0$}

Find a base for B of U where the coefficient of X in every polynomial at the base is equal to -200

I have tried finding a general expression: ax^4+bx^3+cx^2+dx+eAnd tried using x=-1 and get some kind of expression out of the general one, but I got to nowhere with that.

Now cause of the dimU=3  I know the base needs to be 3 linearly independent vectors and I can guess them but I want to do it the right and full solution using a general expression.

Thank you all!


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