What mathematical operation are you trying to undo when you factor a polynomial?

The answer is: The mathematical operation that you are  trying to undo when you factor a polynomial is called "Distributive property".

 An example of the Distributive property is shown below:

 (x-1)(x+2)=0
 x²+2x-x-2=0
 x²+x-2=0

 If you have the polynomial x²+x=2 and you want to factor it, you obtain:

 x²+x=2
 x²+x-2=0
 (x-1)(x+2)=0
 x1=1
 x2=-2

 This is how you undo the distributive property and it is a perfect method to simplifying equations.