Question

use the given zero to find the remaining zeros of each function.

$f\left(x\right)=x^3-4x^2+4x+16$ zero = 2i

Short answer

The zeros of the polynomial is$4,2i,-2i$

Step-by-step solution

Given information

We are given$f\left(x\right)=x^3-4x^2+4x-16$

Find the roots by factoring

Consider,

$$\begin{gathered} x^3-4x^2+4x-16=0 \\ {x}^2(x-4)+4(x-4)=0 \\ (x-4)(x^2+4)=0 \\ (x-4)(x-2i)(x+2i)=0 \end{gathered}$$

Conclusion

The zeros of the polynomial is$4,2i,-2i$