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To write a factored form equation for a cubic function with roots -2 and 3 + i, think of complex roots as coming in pairs. We have -2 and 3 + i, so there's also 3 - i. Now, let's make our equation using these pairs.

Now, we can write the factored form equation f(x):

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Simplify each factor:

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Now, multiply the factors:

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Next, use the difference of squares formula (a^2 - b^2 = (a - b)(a + b)) to simplify the complex factors:

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So, the factored form of the cubic function with roots -2 and 3 + i is:

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