Find the dimension of the vector space V and give a basis for V

V = {p(x) in P2 : p(0) = 0}

*P2 denotes polynomials of degree less than or equal to 2

Sol:

standard basis of P2={1, x, x^2}

let p(x)=a+bx+cx^2

then p(0)=a+0+0 ====> a=0,

do we through away 1 here?

hence

I got Vdim=2 and basis {x, x^2}, but have a feeling that its not correct