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