Factoring Trinomials

When exploring factoring trinomials, it's essential to consider various aspects and implications. Factoring Trinomials "Slip and Slide" Better Explained : r/math - Reddit. I've been reading up on factoring methods and while "slip and slide" is very cool, I didn't think the proof was clean enough. The Method Quickly… Similarly, why is factoring polynomials so hard?

: r/mathematics - Reddit. Factoring quadratic polynomials, at least, is really easy. Just use the quadratic formula. Factoring cubic polynomials is much more involved; factoring quartic polynomials is pretty much as complicated as cubic polynomials, and factoring polynomials of higher powers is actually impossible, mathematically.

At least this is true in one variable. Similarly, how much math work is trial-and-error? In relation to this, : r/learnmath - Reddit. Factoring trinomials is the opposite, it's very 'brute force' and not satisfying because I spend 5 minutes dancing around the right guess before finally figuring it out by luck.

Impossible to understand factoring polynomials. Anyway, not trying to be mean, but factoring is just doing multiplication backwards, and in a lot of cases it boils down to making some educated guesses and then performing multiplication to see if you're correct. So if you haven't mastered multiplication of polynomials, factoring is going to be next to impossible. Additionally, lesson plan is titled "Factoring Trinomials by Trial and Error"....

I’ve never heard of anyone spending time factoring integer-coefficient trinomials past that class. Doing a little is good practice, but useful factoring usually involves more complicated expressions or specific forms like (a-b) (a+b). This perspective suggests that, so it’s more of a lead-in to more complicated algebra. A computer can factor your trinomial.

This perspective suggests that, does anyone teach factoring this way when a>1? I teach precalc so my students initially learned factoring in a prerequisite course. In my experience, most of them cannot remember whatever method they were taught.

They called this one "slip and slide" and the name of it is what they recall, not the method. This perspective suggests that, in my career I have taught guess & check, box method, fishbowl method, key number & split middle term method. I have found that guess ...

What's you preferred method of factoring polynomials? I only know two methods of factoring right now, completing the square, and then having the box method I think its called where you draw four boxes and on the two axis you try to figure out how they will create the function you're factoring. I prefer the box method because it's a lot easier ...

Anyone else think there's way to much emphasis on factoring ...