Factoring Trinomials

Factoring a trinomial that has a leading coefficient other than 1 can be annoying and time taking.
In the video, I show a method that is not taught in most high schools in the USA.
The lesson also includes how to factor trinomials with leading coefficient of 1.

[EdwardKilner]

I’m 78 and never learned this in high school nor engineering school. Don’t have a strong need to know this method, but it brought a big smile to my face. Thank you!

[sherriclowe]

I've been teaching algebra for 38 years and I have never seen this method before!! I am using it in my lesson on Friday. Thank you, Professor H. I am now a subscriber.

[sovietunion]

No shit talks, gets right to the point, very easy to understand and much easier than what my school had taught me, Thank you very much professor

[parkerboyce]

Holy crap... I'm here the night before the test, and this guy is my lord and savior. Thank you sir.

[SharpeCreations]

Highschool Algebra Teacher here and my kids are going to love me when I show them this! Thank you!

[brianjacobs]

I'm 69 years old and still learning. Very grateful for your videos. Please keep doing it, sir.

[mr.x]

Need to say WOW again, you are correct that I've never seen it quite like this. YOU MAKE MATHEMATICS ENJOYABLE AGAIN. Thanks Dr. H

[DavidRobinson-rjsp]

I'm an Engineer and have never seen factoring quadratic trinomials in this way.

BRILLIANT and in the toolbox.

[luisclementeortegasegovia]

Four minutes of great explanation! Thanks professor 👍

[junesantos]

I'm a Senior, everytime my granddaughter ask me about Math/Algebra, I always turned to your channel to make sure I did it right.. Thank You for the very clear and easy catch up on details of solving the problems.. Always refresh my past memory of Math Solving.

[ItzASecretBoi]

You single handedly managed to teach me how to do this in 2 minutes, I've spend my WHOLE day researching this topic, rewatching the materials my teachers have given me, I've been attempting their methods for so long to no avail.

All I can say is thank you, this is a major weight off my shoulders, especially since I'm no good at math, sometimes I wish I could be taught anywhere else besides the US, so many things feel needlessly complicated, and it leads to me giving up hope sometimes.

[RateOfChange]

Nice one.
But I prefer the good old sum and product method, followed by the factoring by grouping method, which is faster:

12x^2 + 17x + 6
The coefficients A and B and the constant term C are as follows:
A = 12
B = 17
C = 6
If you multiply A and C you will obtain 72, as Mr H did. Then you find the two numbers that multiplied will give us 72 and added up will be equal to the coefficient B, which is 17. These numbers are 8 and 9, as shown in the video.
Finaly, rewrite the expression using these numbers and finish up factoring by grouping:
12x^2 + 8x + 9x + 6
= 4x(3x + 2) + 3(3x + 2)
= (3x + 2)(4x + 3)

For the curious, a simple demonstration of why this works:
Given the following product, let's use the distributive law:
(ax + b)(cx + d)
= ac(x^2) + adx + bcx + bd
Now we combine the terms that contain x to obtain a quadraditc equation in the standard form:
= ac(x^2) + (ad + bc)x + bd
The coefficients A and B and the constant term C are as follows:
A = ac
B = ad + bc
C = bd

We know that the product of the coefficient A = "ac" and the constant C = "bd" is equal to "acbd", which can be rewritten as "(ad)(bc)" for better visualization. This means that by multiplying A and C we get the product of the numbers that add up to form the coefficient B.
So if you find what are the numbers that multiplied will result in AC and added up will result in B, you can rewrite the expression using them and finish off factoring by grouping:

ac(x^2) + (ad + bc)x + bd
= ac(x^2) + adx + bcx + bd
= ax(cx + d) + b(cx + d)
= (ax + b)(cx + d)

[Kassidy_quo]

who else is taking an online math class? I am over here trying to teach myself because the software that is supposed to be teaching me, makes no sense at all. I have been watching so many videos on youtube and none have helped. I stumbled across this one, a 4 MINUTE VIDEO, and this taught me so much in such little time. I am so grateful this video is on the internet. keep making great content MR H!! Thank you

[andreasioannides]

I am 47 years old and I've done a bunch of mathematics in high school and Calulus level mathematics later in college but I have never ever seen in my life that way of factoring. The world and especially the kids need more teachers and educators like you Sir.

[fillupdidier]

I was struggling really hard with factoring and really wasn't sure if I was doing it right but I have to say this guy explains it phenomenally

[arnolddezilva]

Some people were just born to do certain things in life. You truly are an amazing educator

[mksarav]

Never learned this method in my school, college, or engineering. Today encountered a similar equation with a>0, when I was teaching factorization to my secondary 2 daughter (she has math exam tomorrow) and watched this video. Beautiful method. Learned something new. Thanks a lot sir. You saved my day.

[KCLIBURN-mjqx]

I, too never saw this method mentioned anywhere by anybody I've ever known but thanks for presenting it and expanding our minds a little bit. I'm mildly pleased to see quite a few people into math. It sure is good to keep the juices flowing and our minds working! Thank you!

[armandelven-dechoux]

My savior. I learnt this method in school and become so confident I thought I could never forget it. 2 years later I did and was faced with the prospect of a lifetime of trail and error. it took me half an hour to find this but I am so gald I did,

thank you

[looalex]

Accidentally watched this video, I found it great! I have never learned factoring like this. So much easy to solve the final answer! I really wish I could have learned this skill back to the 70s when I was studying in secondary school. 👍👍👍