Determine whether polynomials $p(x)$ and $q(x)$ are in the span of $B=\{1+x,x+x^2,1-x^3\}$ where $p(x)=2,$ and $q(x)=3+x^3.$

A$)p(x)$ only

B$)q(x)$ only

C$)$ Both $p(x)$ and $q(x)$

D$)$ Neither $p(x)$ nor $q(x)$

D

A

C

B