SOLUTION: Find a polynomial with the following zeros. 4, 3+2i

Question 844795: Find a polynomial with the following zeros. 4, 3+2i
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Complex roots with imaginary components occur in conjugate pairs.
The root, 3-2i is also a root.

Polynomial with the three roots given is , and you just need to simplify to put into general form.

The multiplication and simplification:
You can more or less use distributive property on each of the complex factors with their imaginary components.

And apply an association on each of those complex factors.

Which neighboring factors are multiplied first does not matter. Take advantage of the difference of square result for the two complex factors with the imaginary components:

-----You can take this one step further and multiply the binomial by the quadratic and put fully into general form.

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