Answer
$P(x)=(x+3)(x-3)(x-\frac{3+3\sqrt 3i}{2})(x-\frac{3-3\sqrt 3i}{2})(x+\frac{3+3\sqrt 3i}{2})(x+\frac{3-3\sqrt 3i}{2})$
Zeros: $\pm3,\frac{3\pm3\sqrt 3i}{2},\frac{-3\pm3\sqrt 3i}{2}$ multiplicity is 1 for each zero.
Work Step by Step
$P(x)=x^6-3^6=(x^3+3^3)(x^3-3^3)=(x+3)(x^2-3x+9)(x-3)(x^2+3x+9)
=(x+3)(x-3)(x-\frac{3+3\sqrt 3i}{2})(x-\frac{3-3\sqrt 3i}{2})(x+\frac{3+3\sqrt 3i}{2})(x+\frac{3-3\sqrt 3i}{2})$
Zeros: $\pm3,\frac{3\pm3\sqrt 3i}{2},\frac{-3\pm3\sqrt 3i}{2}$ multiplicity is 1 for each zero.
