Use the factor theorem to determine whether the binomial x + 1 is a factor of the polynomial function ƒ(x) = 2x3 – 9x2 + 13x – 6.

No, it is not. 
If x+1 is a factor, x=-1 would be one of the zeros. 
Plug x=-1 in the polynomial to see it is results in a 0:
2(-1)^3-9(-1)^2+13(-1)-6=-30≠0, therefore, x+1 is not a factor.