Find dimension and a basis of the following vector spaces: Solution So all polynomials with roots:-1,1 and 2 So multiples of polynomial: f(x)=(x+1)(x-1)(x-2) which is polynomial of degree 3 But degree must be less than 6 So basis is :B={f(x),xf(x),x^2f(x),x^3f(x)} So 4 vectors in basis HEnce dimension =4.