I've been browsing the Math exchange for some time (as well as other sites) looking for an answer in regards to:
"Are there any fundamental differences between factoring an equation, and dividing one?"
I found a decent answer here, but it fails to elaborate in depth on what these differing properties are.
For example, we can factor the equation
2x^2 + 4x - 8
By pulling out a 2, getting x^2 + 2x -4
However, is that fundamentally different in any way from
(2x^2 + 4x - 8)/2
Thank you for any help.