Left factor a grammar that doesn't have a left common factor? I'm working on a question, and it says that I  must left factor the following grammar:
A -> A ∪ B | B
B -> B C | C
C -> C* | D
D -> a | b
What I'm stuck on is, isn't this grammar already left factored? Looking at it, I can't see anything explicitly in the form of S -> αβ1 | αβ2 , which is the form that my book says left-factoable grammars must take.
Let't take the production rules for B. If it were left factorable, wouldn't it have to take the following form?
B -> C B | C
The only way I could think to factor the production rule for B would be this:
B -> B' C
B' -> B | ϵ
However, this doesn't seem like a valid operation on the production rules for B because the common factor is on the right, not the left.
Can someone help me understand this?

Your productions $A \to A \cup B \mid B$ and $B \to B C \mid C$ are left recursive, and have to be factored.
