SOLUTION: Find the remaining of a polynomial with real number coefficients whose degree is 3 and has zeros -3 and 2+i.

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Question 859104: Find the remaining of a polynomial with real number coefficients whose degree is 3 and has zeros -3 and 2+i.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of "remaining polynomial", you mean, "remaining zero". One of the zeros given is 2+i, so another necessary zero is 2-i.

The function from which you can form the polynomial for it is based on the factored form, %28x-3%29%28x-%282%2Bi%29%29%28x-%282-i%29%29. You can perform the multiplication in order to have the product as polynomial.

Part of that will include %28x-2-i%29%28x-2%2Bi%29
%28x-2%29%5E2-i%5E2
x%5E2-4x%2B4%2B1
x%5E2-4x%2B5
-
... and you would then finish by performing the multiplication %28x-3%29%28x%5E2-4x%2B5%29.