Let $B=\{2x,3x+{x}^{2},-1\},{B}^{\prime}=\{1,1+x,1+x+{x}^{2}\}$

Need to find the transformation matrix from $B$ to ${B}^{\prime}$.

I know that:

$(a{x}^{2}+bx+c{)}_{B}=(\frac{b-3c}{2},c,-a)$

$(a{x}^{2}+bx+c{)}_{{B}^{\prime}}=(a-b,b-c,c)$

How to proceed using this info in order to find the transformation matrix?