Given:
A fourth-degree polynomial function has zeros 4, -4, 4i , and -4i .
To find:
The fourth-degree polynomial  function in factored form.
Solution:
The factor for of nth degree polynomial is:

Where,  are n zeros of the polynomial.
 are n zeros of the polynomial.
It is given that a fourth-degree polynomial function has zeros 4, -4, 4i , and -4i. So, the factor form of given polynomial is:


 
           ![[\because a^2-b^2=(a-b)(a+b)]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29%5D)
On further simplification, we get

 
                ![[\because i^2=-1]](https://tex.z-dn.net/?f=%5B%5Cbecause%20i%5E2%3D-1%5D)
Therefore, the required fourth degree polynomial is  .
.