Answer
(a) $-2$, $2-\sqrt 2$ and $2+\sqrt 2$
(b) see graph.
Work Step by Step
(a) Possible rational zeros are $\pm1,\pm2,\pm4,\pm8$
Use synthetic division as shown in the figure, we can find a zero $x=-2$ with a multiplicity of 2.
The function becomes $P(x)=(x+2)^2(-x^2+4x-2)$
Thus, the zeros are $x=-2$, $x=2-\sqrt 2$ or $(0.586)$, and $x=2+\sqrt 2$ or $(3.414)$
(b) see graph.