Because is of degree 2, and is of degree 3, if the first is a factor of the second, then it must be of the form
. Multiplying out the left side, . Since that is to be true for all x, we must have b- c= 2b- 1, 2+ bc= 0, and 2c= -p. Solve the last equation for c= -p/2 and replace c with that in the previous two equations. You should be able to reduce those two equations to a single quadratic equation for p.