According to Sony's website this lens has a zoom factor of 3.8. I currently have an 18-55 lens that came with my NEX-3F that has a zoom factor of ~3.1. Since the 55-210 pics up where the 18-55 leaves off, does that mean you can add or multiply those zoom factors? Is the 55-210 minimum zoom equal to the max zoom of the 18-55 or is there really no correlation between the two lenses?
The X way of measure zoom is misleading because it does not count where things start. It is only a ratio and this is explained in answers to this question.
The 18-55mm and 55-210mm lenses are correlated because the latter at its widest shows the same viewing angle as the former at its longest. The both offer roughly 3X of zoom but outside of at their 55mm positions, show a completely different field-of-view.
The 55-210mm zooms in more, while you can have a lens which zooms out more like the Sony 11-18mm which would ends where the 18-55mm starts. In more photographic terms, we say the 11-18 is an ultra-wide zoom while the 55-210 is a telephoto zoom, while the 18-55 is a standard zoom.