Factor ANY Quadratic Equation Without Guessing | Outlier.org

What if you could solve any quadratic function without any guess-and-check or memorization? This method was actually known by the Babylonians nearly 2,000-3,000 years ago but it's hardly taught in schools. Po-Shen Loh shares how to use the technique, the moment he discovered it, and why it's still such a secret.

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#Precalculus #Po-ShenLoh #FactoringMethod #Outlier

[borisdorofeev]

This guy literally had me smiling the entire time he talked. When people are passionate about something it is infective.

[TheChillennial]

This is the funnest math teacher I've ever seen.

[boredomgotmehere]

This is why YT has become the uni of maths. Thanks Professor Po.

[chocolateangel]

"I think that's how you multiply." 🤣 That's especially funny coming from a math professor -- but I get it. Ever since I learned about the area model of multiplication (and variations of it), I no longer use the standard algorithm. . As for this method of solving Quadratics, it took me seeing it demonstrated, using a graph, before I was able to understand it. Now, it's easy, and I like it. I'm able to visualize a graph in my head now.

[lakshya]

I'm literally crying 😭 right now my biggest fear in maths is quadratic equations and professor just turned suspence into mist thanks outlier ❤️

[kenhaley]

Amazing! In my 77 years I've never seen this method...It's brilliant.

[Tletna]

I liked the joke about how math professors forget how to do basic arithmetic operations. When, I was just an undergrad engineering student I already started to forget, haha.

While I do feel like this was aimed at children, as an adult, I still liked this lesson. It was very simple. He showed clearly how and why it worked. He repeated it twice to show it worked with two different kinds of equations. He showed that we can divide away the a in ax^2 + bx + c. He showed that there will be a + and - version of the answer but that they will be equivalent anyway. His tone was cheerful and kept my attention even if it was a little patronizing sounding. But, he seemed so genuinely into it that I didn't take it as patronizing but just that he really loved what he was doing.

I love math, but even so, sometimes it is hard to make math that is really tedious fun but he sort of made it fun.

What I really liked too is that he was just using basic principles instead of memorization. His simple method would work on almost any quadratic equation. Great video, great teacher!

[johnnyli]

As soon as I look at the title, I supposed this was about the famous Po-Shen Loh method. It's a big pleasure for me to meet through the internet this young talented man. Greetings from a 老外 in China.

[kindreddarkness]

Honestly... for me, this was most useful in actually understanding square roots. This method teaches itself and all it's friends. Well done.

[alessio]

This dude did such an easy thing that none of my teacher never teach me… only 200k views? C’mon YT, give this dude a damn rewards

[mandolinic]

Interesting but leaves more questions than answers. For instance: What do you do when the b (middle) term isn't an even number? What do you do when there is no nice division by the a (first) term? What do you do when the b and c factors are both positive? Or negative? What do you do when the solutions aren't real?
The beauty of the (-b ± √(b^2-4ac))/2a formula is that it works in every case, and IMHO it's easier to remember.

[sigmarule-lbsr]

the fact that this man can see any type of quadratic equation and know its factors right away is absolutely mind blowing. and this coming from a person who is not bad at maths for his age

[krishnachoubey]

Once my maths teacher gave our class a puzzle like —
a+b=11; a·b=28
Find a & b.

He gave some hints & tricks to solve questions & puzzles of such kind, which do come a lot in competitive exams. I generalised it in an equation(not that much work rly) to get a nice equation with a very versatile application—

(a, b) = {s±√(s² – 4p)}/2

Where, s = a+b
And, p = ab
For any number a & b.
(we only know the value of s & p and not of a&b)


From the above question, If we plug in the value of
s=11 & p=28
Then value of a & b can be calculated through—
(a, b) = {s±√(s² – 4p)}/2
= {11 ± √(11² – 4·28)}/2
= {11 ± √(121 - 112)}/2
= {11 ± √9}/2
= {11 ± 3}/2
(a, b) = (7, 4)

Which by cross verification, is correct.



[Derivation of the eqn. in reply section]

[wren]

899 is one short of 900 which is 30 squared so I tried 29 and 31 and it worked

something I did in this surprised me because I just kinda did it in my head and never really thought about it before,

the square of a number will always be one more than the product of one less and one more than the number

a^2 = (a-1)*(a+1) + 1

if you break this open it's obvious how. but I never thought about it this way. In working my way back to finding factors of a product.
For instance, now I know what the product of 1599 can be shown as
39*41

Neat.

[Tetsujinfr]

You are my héro !!! Never found such a clear, generic, and powerful explaination on quadratic eq factorisation. Real neat, such a talent to teach here. You deserve a pedagogy price if that exists. Thanks a million times professor!

[mikeeisler]

3:35 minutes in and you hooked me. This is amazing. Difference of squares is truly the work horse of algebra.

Brilliant

[anuragiyer]

This method was taught in my school even before the quadratic formula

[Lght]

I never knew this till now, I could have just think outside the box, but instead stuck with the idea of only relying on the instructions of the teacher rather than thinking about radical solutions, which really brings out the beauty of math.

[LydellAaron]

6:09 don't ask a professor to multiply: I thought I was the only one with a fear of multiplying on the spot.

[mystyx]

It's surprising how much less advanced Western mathematics seems compared to the methods commonly used by school children in Asian countries.