Using Factoring to Solve Quadratics (Precalculus - College Algebra 18)

[@EvilMAiq]

You know, the most impressive thing to me about these videos is the lesson planning that went into them. The slow addition of a single new idea into each example shows a lot of foresight and knowledge of how people learn. Thanks for the vids.

[@RanBlakePiano]

Well said

[@alhomeronslow5505]

Yes. His ability to articulate the teaching, once all the planning has been completed, is also excellent! Get your degree knowledge in math from Professor Leonard.

[@dorsia6938]

Hi Prof Leonard, you are removing the fog which has been obscuring my understanding of maths for years. I just subbed to your patreon, really awesome material and I feel really lucky that I have access to it. Thank you from the bottom of my heart.

[@travisotwell4747]

I teach Algebra II and college algebra in high school and I teach this method (for the most part) as well. One thing some students still struggle with is finding the numbers on the sides of the x that help you set up the grouping. A coworker showed me the hack of putting the top number into a graphing calculator as y=top#/x. This makes it to where the table that corresponds to the function are all factors of the top. So all students have to do from there is find the numbers on the table that add up to get the bottom #. I am learning from your videos on diff eq for my masters, haha. Thanks for what you do!

[@wachowski9525]

You are literally blowing my mind with that factor shortcut...

[@danceswithdirt7197]

I love it dude. I've just been factoring it for years in my head but I didn't realize the shortcut. Now I've learned something new. :)

[@sineda6659]

On God seeing how that shortcut works was the first time that math has made me feel excited. If only all teachers were Professor Leonard. Thank you so much!

[@LoudSodaCaleb]

Quadratics and knowing how/when to factor them was my ceiling in math, thank you so much for this. I’ve taken so many algebra classes that talked about this subject and it finally clicked. Thanks!

[@calculushorse2644]

That is the coolest technique ever, I've wasted so much time in highschool trying to factor troublesome quadratic equations.

[@hrperformance]

This is a fantastic channel that I always recommend. Thank you so much Prof

[@tasfiaahsan6262]

This is totally true. The short cut that you have shown, works each and every time. Thank you for this trick Professor.

[@cassxavier]

I cannot thank you enough for the fact that you are the sole person helping me understand what is happening in my PreCal class. I had an Algebra 2 course in high school but the teacher was not good at his job and didn't teach any of the concepts that I would have ended up needing for my engineering degree. I truly will never be able to thank you enough for helping me.

[@Abdulrahman-uk9ny]

I can't wait to see your linear algebra course..

[@rayniac211]

I watched this twice and now I'm feeling pretty good about factoring quadratics!

[@simplylokaamv3541]

i really hope professor Lennard sees this , omg I cant express how thankful i am I always thought , i was just stupid at math and when got into cs and i dropped Cal 2 bec i filed my quizzes .....I stared to watch Professor Leonard as string of hope to might pass....I realized that that i can not only pass with a good mark...I finally can understand factoziton, LCD, why we sit = to zero....all the time when i am watching ..its like lightbulb moment ..ohh thats why we are doing what we were doing....thx you so much hope you all the best

[@raiavigil1295]

I'm loving that diamond technique to factor and solve quadratics!! Way easier to wrap my head around. Many Thanks, you are a wonderful teacher!!!!!

[@AriCreighton]

Greatest math professor in the world

[@angelsanchez2779]

Recently became a Navy vet, and this series has eased any and all of my math anxieties that I have going back to school after six years. Thank you, Professor.

[@ianhnizdo4787]

Love watching this man, everything is explained so consicely.

[@jimjim2119]

He is an excellent teacher!

[@Ro.T560]

I can’t believe these videos are free. Thank you

[@jgoemat]

Thanks, love the videos! One thing that messed with my head was that you say the order of the two numbers doesn't matter, but only show the factoring one way. The numbers seem to magically pop out allowing you to factor. Trying it the other way manually I see how that works and I think gives a better understanding of why that happens. For example with `3x^2 + 5x + 2` you rewrite to `3x^2 + 3x + 2x + 2` and factor as `3x(x + 1) + 2(x + 1)` so the `x+1` is in parenthesis and you get `3x + 2` for the other. If you write the other number first it is `3x^2 + 2x + 3x + 2` which factors to `x(3x + 2) + (3x + 2)` so the `3x + 2` is in parenthesis and you get `x + 1` for the other. Neat!

[@MrGrinch1225]

This was absolutely incredible. So glad to have found your channel. Thank you.

[@jessecadena58]

The shortcut is super cool

[@RiseAndGrind991]

hey man i know this was made years ago and your never gonna see this comment but your the only channel i turned my adblock off for i hope it helps and you have a wonderful day! Thanks for the great videos your helping me so much.

[@barath14]

i have my first pre-cal exam this wednesday Feb. 5th, covering completeing the sq, sq root prop, zero factor prop, complicated D=rt and I=Prt problems and this video on factoring has helped me see the picture for factoring, ive been struggling for the past 4 weeks trying to understand this stuff going at a fast pace. thank you so much for your videos!

[@SalmanAhmed-cd5dm]

You may know or not, but you are doing a hell of a job!!! Don't really have any words to describe how much you are helping.

[@socialonly4491]

Wonderful explanation, as always

[@MrPook2k]

I’m 50 and in University attempting calculus 1 (again), but I’ve needed to fill in some important gaps. This video series has been an every day thing for a week now. Excellent work. I actually said ‘holy shit!’ Out loud during the explanation of the diamond method in this video. Thank you sir!

[@UmalkhayrxaashiBarre]

Thank you professor leanard your effort

[@wesrobertson8753]

Wow. This is amazing. Im glad Im going back through precalc with these lectures or I'd have never found this shortcut!

[@Furrburgers23]

I was actually getting the "math chills" when you mentioned them haha Thanks so much for being such a great teacher! Wish i could pay my tuition to you instead of my school because i learn a lot more from you, but ill make sure to become a patreon. Looking forward to your trig content as ill be taking it this semester.

[@barryhughes9764]

Dear Professor Leonard, is there any chance that sometime in the near future you may consider covering and deriving the Euler/Lagrange calculus of variations? As usual thanks for all your videos, from the elementary up to calculus 3, I have watched them all and learn't so much. Kind regards, from a patreon.

[@AyisatLawalShittu]

Yeah 55:35

[@enriqueruiz4191]

Now that is how you teach math! Incredible video.

[@RK-gx5df]

Professor Leonard you are a fantastic teacher! I've always struggled with math but your videos are helping so much. Thank you for doing these.

[@poluefemus]

i always forget how to factor each year, thanks man this is the best method i’ve ever learned, it’s hella fast

[@yevengyklaus7066]

Thank you for what you do!

[@MA-rc2eo]

While I'm by no means consider myself a smart math student, but I do appreciate mathematics and have respect for math teachers. Math teachers create the tools that we use in our lives. Sir thank you for posting this video.

[@lincolndexter9514]

I remember doing pre-calculus...too bad I didn't know about this channel then. It did help when I was in calc 2 and 3 though

[@georgettebeulah4427]

This make so much sense and can relate to it a lot but hope to see more from it and really wish for more video

[@fuzyfuzfuz2]

OMG YOURE THE BEST MATH TEACHER ON PLANET EARTH THANK YOU THANK YOU THANK YOU!!!!!! I always struggled with understanding factoring and this was so helpful!!! I WAS making the mistake of using the wrong shortcut but never understood why. Now I do ❤ Thanks professor Leonard!

[@TheDragoonChannel]

Real analysis 🙏

[@lukepjsmith]

Thank you so much for all these videos I have re learning forgotten stuff from about 10 years ago. Your explanations are very detailed but I have one minor suggestion: at around 38:00 you were talking about changing signs before factoring and transforming the graph, I can see this is where some people might get confused. So, it might benefit from seeing the transformation about the x-axis visually. This will help drive home your point and also reinforce the graph transformations from earlier.

[@Peter_1986]

I love finding shortcuts for as many algebraic problems as possible, so that I can bypass all the tedious calculations, lol.

[@mirandajade5617]

thank you professor

[@chericha]

Wonderful lesson! Thanks again!

[@lloydandersen343]

excellent trick!

[@maths_Simplified_2025]

I really do appreciate the techniques you have shared, the short cut is fantastic. Thank you so much. Wishing you abundance of health and wealth.

[@randomcontents9157]

Thank you so much professor leonard.

[@jabumthembu422]

Thank you Professor Leonard!

[@georgesadler7830]

Professor Leonard, thank you for an impressive video/lecture Using Factoring to Solve Quadratics. These factoring tools have been around forever, however college and high school students should learn short cuts and trial and error methods to make life much easier.

[@rozha3963]

this man is a hero

[@shemuelx]

Excelente tecnica professor Leonard! Thank u!

[@dedkeny]

Your a godsend Professor!

[@plamenyankov2182]

Professor Leonard you've just undone the bad job my high school teachers had done to me, for that one I thank you very very much!

[@Stonehawk]

you managed to explain it in UNDER 3 minutes!

[@briangale404]

I was never taught this method for factoring. Thank you

[@jcesal6457]

Thanks so much for this series! I was kinda was laxidasical through algebra 2 and i am starting pre calc next week, these vids are helping me get back up to speed. How many vids do you expect in the total series?

[@ProfessorLeonard]

Lots! I don't even know how many.

[@jcesal6457]

@@ProfessorLeonard Cool! I look forward to em!

[@nverkhachoyan]

This an amazing technique, thank you professor! I appreciate it a lot.

[@MathswithMuneer]

Always fantastic ❤️

[@ts_1977]

Professor Leonard, when are you going to teach complex numbers - de Moivre's theorem, etc!? Regards ~ from your patreon

[@horizonbrave1533]

@10:18 Live Long and Prosper to you too pal!

[@nadiasultan7893]

Leonard the Great!!!!!!

[@rickhoro]

Incredible!! I hated factoring in H.S. because it just looked like a random grab bag of junk applied at random. Cannot thank you enough for this gift of factoring.

[@bhavyahemnani2243]

Legend

[@stannone7272]

thx leonard im about to be a math fan

[@isaac10231]

I'm doing multivariable calculus but sometimes I like watch the non super high level math content because it gives me insight as to how to teach these concepts.

[@robertcase6475]

The diamond method changed everything

[@_A1Anime]

Hello Professor Leonard, will you ever be making videos on Linear Algebra. Really in Need for that.

[@Peter_1986]

Yep, he will make those videos some time in the near future. He actually talks about that in the video "Professor Leonard's Important Announcement 2019".

[@Lumenxi360]

Thank you

[@laurawestenra]

math is so relaxing.

[@trentnert]

35:40 I paused the video and worked this problem to see if I could do it but forgot to make the first term positive, yet I still got the same solutions and factors. Is this correct or am I missing something? Is making the first term positive meant to just make the whole process smoother? I know these are 4+ years old at this point but you’re helping me so much to prepare for going back to school this fall so thank you!

[@hicarodanrlley149]

To summarize, the square root method WILL ALWAYS WORK whenever b = 0, otherwise we need to use other techniques such as completing the square.

[@mickeyp6639]

thanks for that

[@thangarajselvamani178]

Thank you sir :)

[@chocolateangel8743]

You did a great job teaching this. However, I prefer using an area model over the standard "AC + Grouping" approach. When it comes to your "shortcut," I most often hear it being referred to as the "Bottom's Up" method.

[@kabulkhan2245]

Love you my dear teacher..💓

[@kal5211]

My man

[@elovo4]

Does anyone know a Physics professor that makes KZbin videos as awesome as Professor Leonard? If so, please let me know!!! Thanks

[@Peter_1986]

Jeff Hanson is really good, and he shows just the same passion for teaching as Professor Leonard. He has videos on Statics, Solids and Dynamics, as well as a bunch of other science videos.

[@djt6fan]

@@Peter_1986 Jeff Hanson makes engineering physics courses, Michel Van Biezen has pretty much the entirety of high school physics covered. Both are great.

[@Peter_1986]

@@djt6fan Michel Van Biezen has several videos on a college level as well, like for example Calculus 3, Space Mechanics and the Euler-Lagrange equations.

[@amreshyadav2758]

you are awesome professor, greetings from india.

[@rayj1232]

The greatest professor

[@JordanRugg53]

What camera do you use for your videos? The sound is very good quality

[@nitrouspeed3583]

Does your subscriber count start going up about halfway through every semester?

[@feilongish]

33:00

[@1234larry1]

Since you have an actual equation, not just a term, with the left side = 0 on the right side, why not just begin by dividing the left side by 3 and the right side(0) by 3. The right side would still be 0 and the factor of 3 on the left is eliminated.

[@mohamedberrhili2448]

westside 10:11

[@gt_parker6178]

is there still use for this if you can just use desmos and find the intercepts by graphing?

[@gamesonrack7138]

Km from a country speaks Arabic my math teacher made me hate math but this should've been easy for me but they complicated but, you oh my god are magical profeser

[@GSU_Panther_Nation]

Factoring quadratics is the core of College Algebra and Algebra 2, including intermediate algebra

[@JuanPabloMartinez-b8m]

If you were brazilian then your channel would have some million more of followers and views. I appreciate your hard work, Mr. :)

[@physicsvoice3597]

Plz make course on real analysis

[@sharaudramey9336]

Please can someone explain the details around dividing the diamond method factors by 'a?'

[@REVIEWSONTHERUN]

Nice!✌️

[@techzoneplus]

Bravooooooooooooo.................

[@AyisatLawalShittu]

I’m not even in college but I’m in 5th grade but I do advanced math so I’m taking a calculus course. You are teaching the next generation of engineers, professors, and scientists.

[@hahahahahahhahaha6]

uh huh sure lil bro

[@HeavenlyPress]

33:23, I did

[@si_monster7365]

Why doesn't this work for 16x^2+12x-10?

[@mickeyp6639]

They do: factor out a 2 2(8x^2+6x-5) then find two numbers that multiply to -40(ac) and add to 6(b). You will find 10 and -4 Divide those two sides of the "diamond" by a(8) 10/8 and -4/8 simplify to 5/4 and -1/2 (4x+5 and 2x-1) Solve for them and you get x = -5/4 and x = 1/2

[@unironicaluser1867]

cant wait to understand lmfao

[@bextrekks8354]

min 33:23 - math joy face - :D

[@Clutcch]

18

[@angajasonr.2422]

Nicee

[@surojpaul14]

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