Let's think about P-factor for a moment. The texts tell you that at high AOA, the downward-moving prop blade has a bigger "bite" than the blade on the other side. Very well, for a taildragger on the ground this might contribute to a left yaw on a right-hand rotation prop. But for a tri-gear single, the AOA is near zero on the ground, so P-factor is about nil.
In multi-engine aircraft (except for those with counterrotation such as the PA-39), it's likely that P-factor is a contributor to the yaw on takeoff; On one side, the downward-moving blade is farther outboard from the fuselage centerline (i.e. longer arm) than the other side. The engine with the shorter arm is thus the critical engine for OEI.