Answer
$1,\pm3i$
Work Step by Step
1. List possible rational zeros $\pm1,\pm3,\pm9$
2. Test these values and do not forget about multiplicity (m).
3. We find a zero $1$ with $m=3$ as shown.
4. $P=(x-1)^3(x^2+9)$
5. Zeros $1,\pm3i$
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