Let $V={\mathbb P}_3[x]$ be the vector space of real polynomials in $x$ with degree less than 3. Let $L:V\to V$ be defined by $L(p(x))=-6 p''(x) + 5 p(x)$.
a. Find the characteristic polynomial $f(t)$ of $L$.
$f(t) =$
b. Find the minimal polynomial $m(t)$ of $L$.
$m(t) =$
c. Find the minimal polynomial $g(t)$ of $L$ relative to $1+x$.
$g(t) =$