What is a power factor correction choke (PFC choke) and how does it work?
A power factor correction choke (inductor) would be used to correct a leading power factor (current leads voltage) caused by a capacitive load. Your motor, being an inductive load, will have a lagging power factor (voltage leads current) and therefore its power factor should be corrected by adding a capacitor in parallel with it. 

Edit.
A power factor correction inductor can be added to a linear load (sine wave), which has a leading power factor, to increase the power factor. This type of power factor is known as a displacement power factor because the current is displaced relative to the voltage.

The other type of power factor is known as a distortion power factor where the power factor is neither leading nor lagging. This type of power factor can also be calculated from (real power)/(apparent power) but the concept of cos(phi), used for displacement power factor (sine wave and linear load), is no longer relevant. Distortion power factor being less than unity is caused by harmonic distortion introduced by the non linearization of the waveform due to, for example, a rectifier/capacitor input combination. The harmonics increase the reactive power. This type of low power factor can be improved by the addition of a front-end filter which removes the harmonics and therefore linearizes the load (current/voltage waveform). This harmonics reducing filter could be active or passive, the latter making use of inductors and capacitors.