Answer
The zeros of P(x) are $3, -1+\sqrt6, \text{ and } -1-\sqrt6$.
Work Step by Step
RECALL:
The factor theorem states that c is a zero of P if and only if $x-c$ is a factor of P(x).
$c=3$ therefore $x-c = x-3$
Divide P(x) by $x-3$ using synthetic division to have: