I have a somewhat large Rex Begonia Plant and I am in need of two. I'd like to propagate this plant, but don't have 6 months to do a leaf cutting propagation technique. Does anyone know how I could propagate this plant using the rhizome technique?

Just take a rooted piece and replant it. If you don't have a rooted rhizome you should be able to root one fairly easily. Put it in some good potting soil. Providing humidity would probably help. A terrarium or other makeshift humidity enclosure. Provide plenty of light and keep moist but not overwatered/soggy.

Hi & welcome!

If you cut a piece off of the rhizome and half-bury it on the soil surface in the new pot, it should take root & start growing leaves. I would let it dry overnight after cutting, and pot it the next day.

Alternately, you could unpot your plant, cut the rhizome at a spot where both pieces have some roots & leaves. If doing this, I would repot right away, keeping the wound exposed (and as clean as possible) so it can dry, and wait until the following day to water.

Thank you for the information. Very much appreciated!

Happy to share what has worked for me.

You can root a Rex begonia leaf in water, the root forms at the base of the stem. It roots very easily

Absolutely, but it was specifically mentioned in the opening statements that quicker results were desired. Division is instant, cutting a leafless piece of rhizome would be the next option, with leaf props being at the bottom of the scale, if the goal is quickest results.