Let $V$ be the vector space ${\mathbb P}_3[x]$ of polynomials in $x$ with degree less than 3 and $W$ be the subspace $$W=\text{span} \lbrace x-6-6x^{2},5+9x+x^{2} \rbrace .$$
a. Find a nonzero polynomial $p(x)$ in $W$.

$p(x) =$

b. Find a polynomial $q(x)$ in $V\setminus W$.
$q(x) =$