Factoring Trinomials Using Bottoms-Up

Also see Factoring Trinomials using Trial and Error and Grouping

[Sayian]

Thank god. This method is much easier than trial and error and grouping combined. Thanks so much for this!

[fordsvt]

So, this method appears to be so much easier than "trial and error" (what I call the 'needle in a haystack' method). If that's that case, why is 'trial and error' the primary method that is taught? Thanks for the tip - this just made my day!

[Mathispoweru]

@dan1600m Yes, you must simplify the fraction. If you don't and multiply it out to check it won't be equal to the original trinomial.

[brokenrobotgames]

I was taught the method for factoring that took the original trinomial from ax^2+bx+c to the x^2+bx+ac, but when you get the product of ac you find the divisor where adding equals b, then those two factors replace bx and become x^2+bx+bx+c, then factor by grouping. (I hate fractions). It could also be worth mentioning that ax^2-bx+ac means same sign, both negative, you get that from +ac to tell you same sign, and -bx to tell you the result is negative. so if you have 12x^2-11x+2, then its same sign, difference of two numbers. if +c (same), if -c (different), if -bx (negative result) if +bx (positive result). to +bx-c means different signs smaller number is negative. -bx-c is different signs larger number negative etc etc.

[sakuraharuno]

This video is great, I learn a lot from these!

[estrielmoo]

My god dude. This video helped so much. Thank you!

[danm]

would it matter if you did not simplify the fraction? For instance around 4:00 in the video would it have been ok if you left it as (15x + 10) (15x - 9)?

[autumn_wol_f]

Although this method is easy, we sometimes call it the "voodoo" method because it seems to work by magic. I sat down with paper to prove that it works, and it is very complicated. No student who learns this method has any idea how it works

[gamerprof]

The AC method is much better. This is awful.