The polynomial f(x) is given by f(x) = x^3 + 6x^2 + x - 4. Show that (x + 1) is a factor of f(x).

To show that (x + 1) is a factor of f(x), we need to show that f(-1) = 0.

Substitute x = -1 into f(x):

f(-1) = (-1)^3 + 6(-1)^2 + (-1) - 4
f(-1) = -1 + 6 + (-1) - 4
f(-1) = 0

Since f(-1) = 0, we can conclude that (x + 1) is a factor of f(x).

To show that (x - 1) is a factor of f(x), we need to show that f(1) = 0.

Substituting x = 1 into f(x), we get:

f(1) = (1)^3 - 6(1)^2 + 1 - 4
f(1) = 1 - 6 + 1 - 4
f(1) = -8

Since f(1) ≠ 0, (x - 1) is not a factor of f(x).