How do I know where I would be using factoring as opposed to rational zero theorem? Do I do Descartes rule of signs to get how many positive/negative and then attempt RZT to get rational zeroes, then if the amounts don't match up, try factoring it?
On top of that, how do I know whether to complete the square or "factor it out" (is there an easy way to do this for non-(x+a)(x+b)-esque ones?)? IIRC, quadratic eq is used only for $ax^2+bx+c$-type where maximum degree is 2 -- do I factor degrees > 2 into some kind of (x+a)(ax^2+bx+c) and then attempt quadratic equation if it's above 2 degrees?
Thanks, much appreciated