Given two sets

$\displaystyle U = \{p(x) \in R_4[x] { | } p(2) = p(-2) = 0\}$

$\displaystyle W = \{p(x) \in R_4[x] { | } p(1) = p(-1) = p(0) \}$

Prove $\displaystyle R_4[x] = U \oplus W$

Can someone please give some direction on how to solve this.

Thanks!