I guess I am not the only one, Annette, that is perplexed about cutting peony roots. I don't see how vendors produce those clean tidy roots they send. Mine (Border Charm and Lemon Chiffon) looked like the Texas Chainsaw Massacre when I was done. I guess the proof will be if the six pieces I came up with (it broke up badly when I was trying to get it out of the ground where it had been for around 5 years) when I finally got it out of the ground. So the 'dividing' was done in the digging up process. All the pieces, and some are fairly large, have eyes. Don't necessarily want four (gave two away) of them, but for the time being I am using them to form an edge (it is somewhat draping in from) in a new garden. If they survive I will give the extras to friends next spring.
