Chapter 5.8, Problem 1E

In Exercises $1-6$, the linear transformations $S,T,$ and $H$ are defined as follows:

$S:P_3\to P_4$ is defined by $S\left(p\right)=p\text{'}\left(0\right)$

$T:P_3\to P_4$ is defined by $T\left(p\right)=\left(x+2\right)p\left(x\right)$

$H:P_4\to P_3$ is defined by $H\left(p\right)=p\text{'}\left(x\right)+p\left(0\right)$.

Give the formula for $S+T$. Calculate $\left(S+T\right)\left(x\right)$ and $\left(S+T\right)\left(x^2\right)$.