I am sure there is a better strategy that someone smarter than me would use, but I am not that person.
I am trying to factor
$$x^2 - 3x^2 - 4x + 12$$
I don't know how so I attempt to guess with long division. I cheat and look at the answer so find out one of the factors to save myself time, so I try x - 2
I am not sure how to type out long division but I get
$$ x - 2 | x^3 - 3x^2 - 4x + 12$$
so I know I can have an $x^2$ for how many times x goes into the leading term.
Subract it all and I am left with
$$ x - 2 | -x^2 - 4x + 12$$
I know that the leading term goes into the inner leading term $-x$ times or however you say that.
$$ x - 2 | - 2x + 12$$
$$ x - 2 | 8$$
Now I don't know what to do, how did this go so wrong? I have $x^2 - x -2$ ontop and I have a remainder of 8. This can't be right, I cheated so I know that this should be a factor.