SOLUTION: Why do we even factor? What is the purpose of it? What do we use it for?

1.  If you have no use factor, do not use it.   (It is a joke, of course. But it fits the tone of your post).


2.  Imagine that you need to solve this equation

     = ,

    and you have no a piece of paper to write the quadratic formula.

    But you can solve it mentally, by factoring the left side as (x-3)*(x-7). 
    Then you easily get the roots 3 and 7.


3.  Now imagine that you need to solve this cubic equation 

     = .

    How can you do it?

    Again, apply factoring and factor the left side as (x-1)*(x+1)*(x-2).

    Then you easily find the roots 1, -1 and 2.