I believe a 'distinct 0' refers to one solution of . Two distinct 0's would then be 2 seperate solutions.
A removable discontinuity: When you put R(3) into the equation, you get . However, when you factorise R(x), you can take out a factor of , eliminating this undefined solution, so the discontinuity is removed.
Essentially it's just when you have factors that cancel.
Equal 0's are repeated roots.