A polynomial function with zeros 4​, 5i​, and −5i is ​f(x)=x3−enter your response herex2+enter your response herex−enter your response here.

Answer 1

x=4 = one zero

x-4=0 is one factor

x=5i = another zero

x^2 = -25

x^2 +25 = a second factor

x^2 =-25

x = +/-5i the conjugate pair of two imaginary zeros

multiply them together to get the cubic polynomial function

f(x) = (x-4)(x^2 +25)

f(x) = x^3 -4x^2 +25x -100