Chapter 6.3, Problem 44E

Let $T:P_2\to P_4$ be the linear transformation $T\left(p\right)=x^{2}p$. Find the matrix for $T$ relative to the bases $B=\left\{1,x,x^2\right\}$ and $B^{\prime }=\left\{1,x,x^2,x^3,x^4\right\}$.