Question

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

$g\left(x\right)=x^3+3x^2+25x+75;zero:-5i$

Short answer

The zeros of the polynomial is$5i,-5i,3$

Step-by-step solution

Given information

We are given an equation$g\left(x\right)=x^3+3x^2+25x+75$

Find the zeros by factoring method

We have,

$$\begin{gathered} g\left(x\right)=x^3+3x^2+25x+75 \\ {x}^3+3x^2+25x+75=0 \\ {x}^2(x+3)+25(x+3)=0 \\ (x^2+25)(x+3)=0 \\ (x-5i)(x+5i)(x+3)=0 \end{gathered}$$

Conclusion

The zeros of the polynomial is$5i,-5i,3$