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Sounds like this is part of a larger assignment in which you've presumably already been asked other questions similar to this. You'll need to be more specific about what you've already explored for us to understand what the "several other possible combinations of factors" refer to. It would also be helpful if you explained what part you're stuck at.
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I'm not 100% sure what the question is asking for (it would have helped to see the whole statement of the problem). But a simple example of a quadratic with complex roots is x\^2 + 1. So an example of a 4th degree polynomial with this as a factor would be x\^4 - 1, which has roots +1, -1, +i, -i, and can be factored as (x-1)(x+1)(x\^2 + 1).

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