What does "factorize" mean?

When we learn maths, we have receive the problem to factorize some expresions or numbers, but what does it means?

Factorize is the process by which we convert anything (a number or algebraic expresion) in a multiplication.

So, if we must factorize a number, we will transform that number in a multiplication of primes numbers:

factorization of 24 = 2·3·4

And factorization of an algebraic expresion, is another expresion transformed in a multiplication instead of an addition:

x2 + 2x + 1 = (x+1)·(x+1)

Remember: factor is a part of a multiplication, in the same way that a summand is a part of an addition.