For the following linear operator T, I have to test T for diagonalizability, and if T is diagonalizable, I have to find a basis B for V such that $\displaystyle [T]_{B}$ is a diagonal matrix

$\displaystyle V=P_{2}(\mathbb{R})$ and T is defined by T(f(x))=f(0) +f(1)(x+x^2)

any help?