Use the factor theorem to determine whether the binomial x+ 1 is a factor of the polynomial function f(x)= 2x^3-9x^2-13x-6.

The factor theorem requires that you plug in the value of x in question and see if the "answer" you get is a 0.  If it is, that number is a 0 of the polynomial and if there is a remainder, then it's not a factor.  You could also accomplish the same thing by doing synthetic division.  When you plug in -1 to your polynomial you get a result of -4.  That means that x + 1 is not a factor.