You have the following function:
f(x) = x^3 - x^2 - 3x - 1
Consider that factor theorem states that if the remainder of the division between f(x) and x-a is zero, then, x-a is a factor of f(x).
In this case, you have that the division:
x^2 - 2x - 1
x + 1 l x^3 - x^2 - 3x - 1
-x^3 - x^2
-2x^2 -3x - 1
2x^2 +2x
-x - 1
x + 1
0
The remainder of the previous division is zero, then, x + 1 is a factor of f(x)
