To solve the problem we must know about the Remainder Theorem.
<h3>What is the Remainder theorem?</h3>
According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.
The roots of the function are 2, 1, and -2.
Given to us
- One factor of f (x) =
is (x – 2).
<h3>What is the quotient of the function?</h3>
We know (x-2) is the factor of the function, f(x) =
,
therefore,
![f(x) =4x^3-4x^2-16x+16 = [(x-2) \times quotient] + Remainder](https://tex.z-dn.net/?f=f%28x%29%20%3D4x%5E3-4x%5E2-16x%2B16%20%3D%20%5B%28x-2%29%20%5Ctimes%20quotient%5D%20%2B%20Remainder)
As (x-2) is the factor of the function, therefore, the remainder will be zero for the equation,


<h3>What are the factors of the function?</h3>
Solving the quadratic equation,

Hence, the roots of the function are 2, 1, and -2.
Learn more about Remainder theorem:
brainly.com/question/4515216