Find a cubic polynomial given zeros and leading coefficient

Firstly, we can ignore the leading coefficient of 1, as 1 is always assumed to be the leading coefficient in the absence of another leading coefficient. Next, we now that every imaginary zero has to have a negative counterpart. Therefore, our zeros are 2, 3i, and -3i. Next, we put these zeros into factored form. This gives us f(x) = (x - 2)(x - 3i)(x + 3i). Now, all we have to do is multiply out and combine all like terms. This gives us an answer of f(x) = x^3 - 2x^2 + 9x - 18.

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