Factoring Quadratics WITHOUT Guessing Product & Sum

0:00 x^2+32x+92
7:00 x^2-6x-91
10:10 x^2+9x+20
12:53 2x^2-7x-4
15:42 x^2+8x+4
17:50 x^2+4x+10

[saturday]

Okay, wow. This method should've been taught in schools. Incredible!

Edit: I am actually lost for words. Sounds like glazing but it isn't

[claude]

My only suggestion is that "c" is used to define two different things: The third "element" of the quadradic equation and the "constant value" added to or subtracted from the second element of the quadratic, b. To help prevent confusion, I would suggest calling the second constant value "k", so we don't have two c's with different meanings.

[fgvcosmic]

This is pretty much just how the quadratic formula works. This is how the quadratic formula should be taught, in my opinion; by starting with this as motivation

[danielnegussie]

It is called the Poh Shen Loh method. A math professor named Poh Shen Loh discovered this method. The math professor himself said he found this method buried in a very very old Math book.
Here is the link

[zulfiqarali]

Love this. So much of boring guessing work of stone age in school.
m = sum/2 + sqrt((sum/2)^2 - product)
n = sum/2 - sqrt((sum/2)^2 - product)

[angelviloria]

I came here to refresh my memory on factoring so I can begin teaching my girls (8th & 6th grades).
I love this method because I hate ever having to say “guess and test”. I always look for methods/process or creat one.
This is excellent. I can’t wait to teach it.

[bjornfeuerbacher]

You can also do it in an another way, which in the end is essentially equivalent to the one in the video: first complete the square, x² + 32x + 192 = x² + 32x + 16² - 16² + 192 = (x + 16)² - 64. Then write this as a difference of squares: (x + 16)² - 64 = (x + 16)² - 8² = ( (x + 16) + 8 ) ( (x + 16) - 8 ) = (x + 24) (x + 8).

[Parasuraman-eywo]

Very nice. Someone was smart enough to think if this and formalize, removing guess work.
I would still factorize mentally in terms of sum and product, and in the case of large numbers that are difficult for me to break down that way, I would use this procedure.
Appreciate this new and simple way.

[DaniCanales]

I haven’t even been taught factorisation of quadratic formulas yet, but found this video flabbergastingly interesting and really easy to understand.

[rainerzufall]

This is just a manual execution of the abc or pq formula (there are many names for it). Still impressive.
For simplification I use a = 1 => pq formula for x² + px + q = 0
=> x_{1/2} = - p/2 +/- sqrt( (p/2)² - q )
(x - x_1)(x - x_2) = 0 => m = -x_1 and n = -x_2. That's p/2 -/+ sqrt( (p/2)² - q ).

[Chemest_a]

Yall this is literally the quadratic formula broken down into steps. Fire video tho!

[soilsurvivor]

Great method, and VERY well-presented! Just wordy enough without feeling like you're dragging out minor details. Concise, but not sparse. Thank you!

[ASINGH-lieq]

You explained so good, I am astonished to see this, we never learnt this in school .it is really amazing . thanks .

[unknwonboy-fmei]

we are literally solving a quadratic, to solve another quadratic . Although the approach is nice.

[Sarutolity]

Sending this to every math teacher I’ve ever had 🔥

[mr.cabbage]

This is a fun video, I found the general form for this method by not plugging anything in where
If there is a coefficient on x^2 divide it by every term and put it on the outside of the formula
a(x^2+(b/a)x+(c/a))
We can treat b/a as “b” and c/a as “c” for the formula

[edobolo-hq]

i've had thoughts of this but never found a way to make them useful to my math classes, well until i found this video i could actually do something with it. THanks!

[DaneBrooke]

Wonderful video. Since this amounts to using the quadratic formula for writing the factors of the quadratic, you could have just gone for "How to write the factors of a quadratic by using the quadratic formula". And *that* would have been a wonderful video. And nobody would have guessed or checked anything.

[Dsonsee]

Thanks so much for this method! I teach in highschool and even though I've explored alternatives, I never thought of something so elegant.

I especially like that it takes away the arbitrariness of using the quadratic roots equation, or the frustrating guesswork of assigning numbers and seeing if they work.

[neitoxotien]

Hmmm... I love this method, since back in the day I love Factoring than Quadratic formula. This method gives me a new ways. Thank you.