I used to build a cheatsheet of all the formulae or parts I didn’t have memorized, then only study that sheet, then next session make a new sheet removing the parts you now can do from memory. Repeat until day of test you don’t need to look at any of the sheets to know the all methods.

Do as many exercises as possible. Algebra is pure practice.

Don’t mess with computers or AI or other distracting crap. Do ALL the exercises in your textbook. Then get another textbook covering similar material but with different exercises, and do those. The idea is not to do exercises on topic X until you can get it right. Rather it’s to do them until you can’t get it wrong.

Schaum’s Outlines used to be good for upper division college level math. IDK what they have for intro level like you’re describing.

For the factorization you mention, look at the roots of the polynomial, i.e. x^3+1=0. So the roots are the (complex) cube roots of -1. One of those cube roots is -1 itself, i.e. x+1=0. So that is one of the factors: x^3+1 = (x+1)(something). So then figure out what (something) is.

A trick I was taught very young was to suck on a mint candy, and then when you actually have your test, to also bring a mint candy with you.

The story I was told is that mint causes the blood vessels in your face and head to dilate, so your brain gets a little more oxygen.

Then the olfactory and taste sensation being the same from when you were studying to when you were actually being tested on the topic can help your brain remember the information and recall it when it’s needed.

I cannot prove that this has worked, but for me at least I’ve always been extremely good at tests doing this and maybe that had some part in it.

Everyone has their own best learning methods so what works for me doesn’t necessarily work for you. But here’s my most general advice:

Practice + a good amount of rest so your brain actually processes what you learned during practicing. Homework assignments are usually good practice materials.

While practicing: write down all rules/methods that you forgot on a sheet so you have them all at one place and can come back to them later. Writing the rules down also makes you memorise them better.

Practice, practice, practice.
This is something where AI might be helpful. You can ask it to make you a practice test. Make sure to give it the proper parameters for your course, so you don’t get bullshit questions or unsolvable questions.
If you don’t trust AI, you can find practice tests online. But the same applies, they might be too easy or too difficult for your situation.