How does left-factoring prevent backtracking?
Suppose the input is ab. In compiler terms you have two tokens a and b which are read in linear sequence. So, when you read a it is not clear which production rule to apply since you have three possible rules which begin with a: $A \rightarrow ab \mid ac \mid ad$. To choose the right production rule you need check all possible rules which is done by backtracking. 

However, if you factor this grammar  then you have only one production rule which begins with a: $A \rightarrow aB$ which is the only single possible rule and thus there is no need in backtracking.

Nondeterminism, when parsing, can be resolved using lookahead technique, where left-factoring is one of the steps in order to transform the initial grammar into $LL(k)$-grammar.  For more details please read about $LL(k)$-parsers.