Using the Factor Theorem, determine which of the following is a factor of the polynomial f (x) = x3 – x2 – 3x – 1.

One factor is x+1.

Step-by-step explanation:

f(x) = x^3 - x^2 - 3x - 1.

The factor theorem states that if x-a is a factor of f(x) then f(a) = 0.

Try x = 1 (to see if (x-1) is a factor:

f(1) = 1 - 1 - 3 - 1 = -4.  This is not zero so x-1 NOT a factor.

Try f(-1) = -1 - 1 + 3 - 1 = -3 + 3 = 0

So x+1 is a factor.