Consider the vector space V of polynomials with real coefficients of degree less than or equal to 2. Say, justifying the answer, if the following subsets of V are vector or affine subspaces.
$(i)$ The subset $U ⊂ V$ of the polynomials divisible by $x - 1$
$(ii)$ The subset $L ⊂ V$ of polynomials with a known term equal to 2018.
For $(i)$ we know since $f(x)=x-1$ is a polynomial with integer coefficients then given the following generic polynomials $p(x)$ and $q(x)$, $U$ will be all the polynomials $q(x)$ such us $p(x)=f(x)q(x)$. From here, I believe I should verify its a subspace by checking its closed under addition and scalar multiplication and that zero belongs to $U$
For $(ii)$ I'm not sure how to show that its an affine subspace, neither I understand well the differences comparing with the subspaces. I'll be very thankful if someone can clarify this conceptually and help me with what I should do.