Find a basis $\lbrace p(x), q(x) \rbrace$ for the vector space $\lbrace f(x)\in{\mathbb P}_3[x] \mid f'(-6)=f(1) \rbrace$ where ${\mathbb P}_3[x]$ is the vector space of polynomials in $x$ with degree less than 3.
$p(x) =$ , $q(x) =$