Find dimension and a basis of the following vector spacesSol

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