Find all zeros of the polynomial f(x) = x^3 - 4x^2 - x + 4.

Step 1: Group the terms.

Start with:
f(x) = x^3 - 4x^2 - x + 4

Group the first two terms and the last two terms:
(x^3 - 4x^2) + (-x + 4)

Step 2: Factor each group.

Factor x^2 from the first group:
x^2(x - 4)

Factor -1 from the second group:
-1(x - 4)

So:
f(x) = x^2(x - 4) - 1(x - 4)

Step 3: Factor out the common binomial.

Both terms contain (x - 4):
f(x) = (x - 4)(x^2 - 1)

Step 4: Factor the difference of squares.

x^2 - 1 = (x - 1)(x + 1)

Therefore:
f(x) = (x - 4)(x - 1)(x + 1)

Step 5: Set each factor equal to zero.

x - 4 = 0 gives x = 4.

x - 1 = 0 gives x = 1.

x + 1 = 0 gives x = -1.

Therefore, the zeros are x = -1, x = 1, and x = 4.