Let [math] be the vector space of all polynomials of degree 2 or less, and let [math] be the subspace spanned by [math] and [math].

  1. The dimension of the subspace [math] is .

  2. Is [math] a basis for [math]? Be sure you can explain and justify your answer.

  3. A basis for the subspace [math] is [math] [math]. Enter a polynomial or a comma separated list of polynomials.