SOLUTION: Form a third degree polynomial function with real coefficients such that -5+i and -8 are zeros????

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Question 1137924: Form a third degree polynomial function with real coefficients such that -5+i and -8 are zeros????
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-5-i%29%28x-5%2Bi%29%28x%2B8%29
From this, just basic algebra, and fact that i%5E2=-1.

%28%28x-5%29-i%29%28%28x-5%29%2Bi%29%28x%2B8%29
%28%28x-5%29%5E2-i%5E2%29%28x%2B8%29
%28%28x-5%29%5E2%2B1%29%28x%2B8%29
%28x%5E2-10x%2B25%2B1%29%28x%2B8%29
%28x%5E2-10x%2B26%29%28x%2B8%29----------choose either a lattice method, or distributive property...
x%5E3-10x%5E2%2B26x%2B8x%5E2-80x%2B208
x%5E3-10x%5E2%2B8x%5E2%2B26x-80x%2B208
highlight_green%28x%5E3-2x%5E2-54x%2B208%29