Still astonishing that you remember this stuff.
Unfortunately, your basis cannot produce x^2 - x - 2.
_____________________________________________
\begin{align*}p(1) = 0 &\iff (x-1)(ax + b) = 0 \quad [\text{where }a,b \in \mathbb{C}]\\ &\iff ax(x-1)-b(x-1) = 0 \\ &\iff \mathrm{span}\{x-1...