Hi, I'm just looking for a suggestion on how to go about solving this. I'm not looking for the answer to the question, I have that in the back of the textbook. This is in the review of the chapter Algebra 1. I've covered all the sections and done all the exercises with only a few questions I couldn't solve on my own. I just really don't know where to go with this one. The question is:

If x^{2 }+ bx -2 is a factor of x^{3 }+ (2b - 1)x^{2 }- p, find the two possible values of p (where p is a real number).

I'm not looking for the answer to the question. I'd really appreciate a hint on how to tackle the problem myself. I've covered linear simultaneous equations, polynomials, factors inc, the factor theorem, factorising cubics and rational functions so far. I feel like I should be able to do this but I'm really stuck with how to proceed with it. I tried long division but was unable to get past the first line. Do I need to simplify first? Is it possible to solve it this way?

Thanks.