In Algebra, I've been taught to factor polynomials by grouping. Here is an example:
$$x^3-2x^2+x-2=x^2(x-2)+1(x-2)=(x^2+1)(x-2)$$
I'm wondering if this is an effective method because when they give us problems, the grouping tactic is very obvious like above. But is it good for problems in general that are more than just homework for section 3.7 (just a random number)?
IMO, it is not very effective, and methods like rational roots theorem should usually be used over this one. To me, it seems to be a 'lucky' case that one could use this.