ANSWER
The roots are -2,1 and 2
EXPLANATION
The given polynomial function is
[tex]f(x) = 4 {x}^{3} - 4 {x}^{2} - 16x + 16[/tex]
It was given that, (x-2) is a factor of the polynomial.
From the Remainnder Theorem this implies that f(2)=0.
We can rewrite the given polynomial as;
[tex]f(x) = (x - 2)(4 {x}^{2} + 4x - 8)[/tex]
[tex]f(x) = (x - 2)(4 {x}^{2} + 4x - 8)[/tex]
[tex]f(x) = (x - 2)(x + 2)(x - 1)[/tex]
Hence the other roots are:
[tex] (x - 2)(x + 2)(x - 1) = 0[/tex]
[tex]x=2,x=-2,x=1[/tex]
