Find a polynomial of degree 5 such that both of these properties hold:

Write your answer in expanded form (that is, do not factor f(x)).

Does such a polynomial exist?

I think there is a polynomial that meets these two requirements.

Yes, the polynomial exists:

Thank you so much Alan!

Thanks for showig us Alan,

I tried to do somthing similar using matrices but got in a big mess.

I didn't think of the obvious things. :(