We must have: note there that we may take and as parameters and write and according to the values of them easily.
Just summing both equations we get; and:
Thus: , are the parameters and note that this can be written as: so any vector in that subspace is a linear combination of and (and they are LI) thus is a base and the dimension of the subspace is 2
2.) Let that polynomial is in our set iff: then consider and as parameters, then where are our parameters
thus any polynomial is in the subspace iff it is a combination of and these 2 are LI, thus is a base of this subspace and its dimension is 2.