Factoring (called "Factorising" in the UK) is the process of finding the factors:
Factoring: Finding what to multiply together to get an expression.
It is like "splitting" an expression into a multiplication of simpler expressions.
Example: factor 2y+6
Both 2y and 6 have a common factor of 2:
So you can factor the whole expression into:
2y+6 = 2(y+3)
So, 2y+6 has been "factored into" 2 and y+3
Factoring is also the opposite of Expanding ("Expanding" means removing the ( ) ..)