Given zero "a", (x - a) is a factor of the polynomial. That factor is repeated according to the multiplicity of root "a". Any complex zero is matched by another zero that is its conjugate. Hence all 6 zeros are defined, and our polynomial is
... p(x) = 3(x -4)(x -0)³((x -4)² -(3i)²)
... p(x) = 3x³(x -4)(x² -8x +25) = 3x³(x³ -12x² +57x -100)
... p(x) = 3x⁶ -36x⁵ +171x⁴ -300x³
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The factor pair (x - a - bi)(x - a + bi) can be treated as the factorization of the difference of squares (x - a)² - (bi)². When expanded, that becomes
... x² -2ax + a²+b²