In your example of it says that the basis must have 3 vectors in it
One basis could be
these are linearly independant and span
but you could also have the basis
these are also linearly independant and span
but they both still have 3 vectors.
One way to solve the above problem is to express the polynomials in terms of the standard basis of
The basis is So for example the vector . Now the vectors may look more familiar!