Answer
(a) $x=-1$ and $x=2$
(b) see graph.
Work Step by Step
(a) Possible rational zeros are $\pm1,\pm2,\pm4$, use synthetic division to find three zeros as shown in the figure $x=-1,+2,+2$ so that $P(x)=(x+1)(x-2)^2(x^2+2x+1)=(x+1)^3(x-2)^2$, thus the zeros are $x=-1$ (multiplicity 3) and $x=2$ (multiplicity 2)
(b) see graph.