Due to its wide bandwidth, terahertz (THz) communication technology has the capability to be applied in high-precision positioning and sensing in industrial applications. This paper presents co-polarized and cross-polarized THz channel measurements at 132 GHz in an indoor factory (InF). Firstly, we analyze and model the path loss for both directional and omnidirectional channels. It is found that the path loss exponent (PLE) for horizontal polarization is slightly smaller than that for vertical polarization in the InF. Furthermore, for cross-polarization, certain non-line-of-sight (NLOS) paths have lower path loss than the line-of-sight (LOS) path. Secondly, we calculate the directional and omnidirectional cross-polarization discrimination (XPD). It is observed that the THz channel exhibits higher mean values of the XPD compared to that observed in millimeter wave (mm-Wave) channels. Additionally, we discover a negative correlation between the XPD and the LOS propagation distance. A log-log model is employed to characterize the correlation. Generally, the findings of this work contribute to the precise modeling of polarized THz channels and promote the application of 6G THz communication technology in InF scenarios.