Remark
For the first two terms, factor out 4x^2
For the second two terms, factor out 16
The factor using the difference of squares.
Solution
f(x) = 4x^2(x - 1) - 16(x - 1) x - 1 is a common factor.
f(x) = (4x^2 - 16) (x - 1) factor out 4 from the first factor.
f(x) = 4(x^2 - 4)(x - 1) Factor the difference of squares
x^2 - 4 = (x - 2)(x + 2) Substitute this difference in the line above
f(x) = 4(x - 2)(x + 2)(x - 1)
Answer
The roots are 2, - 2, 1