SOLUTION: Find a polynomial with integer coefficients that has degree 3 and zeros 5, and 2𝑖. [Multiply out to write this polynomial in standard form]

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Question 1162040: Find a polynomial with integer coefficients that has degree 3 and zeros 5, and 2𝑖.
[Multiply out to write this polynomial in standard form]
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
degree 3+
zeros:
x%5B1%5D=+5
x%5B2%5D=2i->complex zeros always come in pairs, so you also have
x%5B3%5D=-2i

f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-5%29%28x-2i%29%28x-%28-2i%29%29
f%28x%29=%28x-5%29%28x-2i%29%28x%2B2i%29
f%28x%29=%28x-5%29%28x%5E2-%282i%29%5E2%29
f%28x%29=%28x-5%29%28x%5E2-4i%5E2%29
f%28x%29=%28x-5%29%28x%5E2-4%28-1%29%29
f%28x%29=%28x-5%29%28x%5E2%2B4%29
f%28x%29=x%5E3+-+5x%5E2+%2B+4x+-+20-> your answer