Can someone show me how to do this problem? I really have no clue.

Given the vector space V of all the polynomials of degree less than or equal to 2. Consider the linear transformation $\displaystyle L: V \rightarrow V$ by $\displaystyle L= c^2+c+I$. For example, $\displaystyle L(x^2)=x^2+2x+2$. Compute det(L) and Tr(L).

I think I have to pick a basis in this vector space, so I can pick the standard basis, but I have no clue how to proceed.