I came across this trick question, and I don't understand the solution to the puzzle. We are asked to simplify the product $$(a-x)(b-x) \cdots(y-x)(z-x),\tag{$*$}$$ and the answer is apparently supposed to be $0$.
I have no idea how this can be, and how one can simplify the above expression. Can someone explain to me why the product $(*)$ simplifies to $0$?