❖ Partial Fraction Decompositions and Long Division ❖

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@christinahmantji4021]

decompose x^5-2x^4+x^3+x+5/x^3-2x^2+x-2 into partial fraction

[@applejackzo]

You got me through Cal 1, 2 and 3. AND you will get me through Differential Equations. I'm watching this to review. You're a gift from Heaven.

[@sheriff8146]

Laplace transform?

[@ishraqomarjwan8501]

AppleJackzO great

[@ICOD73]

One day when I graduate from college and have my own job, I am gonna donate to you. Your videos helped me in several courses from all the calculus courses I took to understanding the math of my higher level mechanical engineering courses. Thank You.

[@hananurrehman]

I have that in my to do list

[@0Janson]

Did u graduate

[@jacold8451]

@@0Janson 😂😂😂been 3 years, I guess he did

[@0Janson]

Ja Cold i hope so hahaha

[@joshsafari8709]

I sleep through class bc I know patrick will teach it better

[@1986Godfrey]

lol

[@abaundwal]

Josh Sarrafian lol no please don't do that. At least make class notes.. who knows, they might come in handy for revision. Good luck! :)

[@changleeyong5098]

Too late for me.

[@admcrableg]

"tired of scrounging youtube for math help?" no, im tired of you interrupting patrick while he's teaching.

[@juanvilla5613]

admd crableg dang that ad is still around after 6 plus years lol

[@maryamkamalkhan]

Still here 4 years later ahahaha

[@hicelina]

I appreciate your existence and the time you take to make these videos.

[@geektech3738]

You posted that video 11 years ago and here I'm learning from it now in 2020 thank you so much man ♥️

[@patrickjmt]

Glad it helped!

[@cd2773]

0:50 Partial Fractions 4:05 Case 1 - Distinct Linear Factors 7:32 Case 2 - Linear Factors, Some Repeated 12:15 - Case 3 - Distinct Quadratic Factors 14:08 - Case 4 - Quadratic Factors, Some Repeated 16:08 - Grand Finale Problem (using all cases)

[@kdogallyall]

Everything my teacher said is finally making sense. I should be paying you my college tuition!

[@zaidalzeiq9840]

ur absolutely right !

[@obieeetleb7764]

true

[@patrickjmt]

glad the class turned out well and a big thanks for recommending me. lots of calc 2 and calc 3 videos as well :)

[@delahkful]

i'm i alnighter mode and honest to god, you made 6 hours of studying short. I have a busy weekend so i won't really get to study the material well the weekend before. it's 2050 and i'm absolutly going to get good sleep tonight. you have no idea how much i appreciate this channel and all the help it has given me over the years.

[@coolguy209111]

you're awesome man. I'm a first year mechanical engineering student and I had some difficulties understanding calculus because my prof didn't teach it very well. I actually learned most of my first term calculus by watching your videos and I have a very good feeling that I did great in my finals. & I actually recommended your videos to most of my friends and they started watching them. Thanks Patrick!

[@diegomaldonado7891]

patrickJMT you da real mvp

[@toddj.2]

Went through all your sequence/series videos, and now all the integral/antiderivative videos, to prepare for an exam. Most excellent, dude!

[@michellelu400]

You're literally better than every math teacher I've ever had. 3/4 of the way through the year, I finally feel like I'm understanding something. Thank you!

[@liewjiashi]

Thank you so much!! Faced a lot of problems in doing my polynomials and your videos helped a lot!! God bless you for making all these precious videos available in KZbin for easy and free access.

[@mollyanngajo8624]

Watching this in 2018. 10 years from when you uploaded it. Still is a much better approach

[@darrylros681]

Thank u so muchhhh been watching u since first year. U already have a place in heaven for helping students that cannot cope up with their teacher

[@patrickjmt]

thanks ;)

[@mollyturnbull118]

ugh I seriously cannot thank you enough for all the help that got me through Calc I and now as I make my way through Calc II!

[@nithinnj]

your awesome man i went to tutoring didn't get it went to class same read the book same your awesome watching this 20 min video learned almost a lesson most teachers are arrogant and don't care thanks for explaining it so well and you do this for free God Bless You

[@missbutter81]

you got me through grade 10, 11, cal 1 and now i'm in cal 2...i literally learned everything from you and just went to class for review.

[@missbutter81]

+Whitelotus i just wish you'd post more videos under your Linear Algebra playlist. Please try to add more!

[@zbro460]

I'm a math major taking Cal2 in my first semester, and this is a life saver! My professor is kind of crap, as he forgets to teach us things that are in your videos, and doesn't even mention these things until a week later, but I'm still doing well thanks to these videos.

[@luvomtati1910]

Man you are just extraordinary you have been helping me since ever in Engineering Mathematics, i am getting Distinctions in maths Bro Because of you thank you so very much PratrickJMT may God Protect you through everything man. You are giving great explaination in everything for me no one like you here on youtube. Thank you man,🙇‍♂️

[@patrickjmt]

thanks for the kind words ;)

[@lfcforever]

It's only fitting i post my first ever youtube comment for you. My utmost appreciation for this awesome work you do. You and your videos got me through my first semester calculus. Mature age uni student from down under. Good on ya mate!!

[@MrBeto081]

Man i love this it took you 20 mins to peoperly explain this and my math teacher just now only took 5 mins to explain it and jumped straight into it -.-

[@mxg5304]

Watch both videos, they are sooooo helpful!

[@ManzanaresDaniel]

That's too bad because I also go to UT and use your videos when I'm doing work outside of class. I also know many other students that do the same. You're a life saver, but you also make the material easier to understand. Thanks!

[@sohoyankee66]

You are just so awesome for taking the time to create and post these video's, Patrick. Thank you so very much for breaking it down nicely. :)

[@vishalshinde5252]

Patrick is a savior to all the math students.

[@Dbird613]

Patrick is simply the coolest Math teacher on youtube.

[@sakif7]

Ive been getting 90s in my calculus class all through out this year through you help, thank you so much :)

[@pixiemirror29922]

I JUST DON'T UNDERSTAND WHY MUST THERE BE DISLIKE-ERS.. ITS A FREAKIN FREE MATHS VIDEO FOR GOD SAKE! err~

[@chrismarklowitz1001]

There always is bro. There always is....

[@leereyno]

Some men just want to watch the world burn.

[@northernskies86]

the dislikers probably really hate math

[@MegaTheDarkdemon]

They be too stupid to understand his math

[@shinesprite4110]

Paul Higdon Maths* in basically every country except America, they say Maths

[@abeerashah4463]

dont know where I would be without Patrick, seriously he's taught me more than my prof.

[@micro529]

Missed my pre-cal class the other day for this lecture..thank you so much for this and for sharing your knowledge with everyone on youtube...for FREE!!! :-) It's greatly appreciated!

[@patrickjmt]

of course, i am saint patrick! they even have a day for me :)

[@MrJimmy1772]

I'm reviewing for Calc 2 finals right now watching this again, but I wanted to let you know that you basically taught me calculus 2 as I couldn't understand my instructor's broken English at MSU.

[@AninOnin]

I watched a lot of your videos for calc 1 (not because my instructor was bad--the pace was just a little fast) and I ended up making the highest grade in it. Thank you so much. I really appreciate you taking the time to make these videos, and I'm sure I'm not the only one judging by the comments xD

[@muhammadsaadbinzahid9496]

Cant believe it was made in 2008 and its still helping people out. LEGEND !

[@LoveDayandAge]

You are the reason I will pass Calc II. You are my god.

[@delahkful]

Praise the Almighty PatrickJMT

[@harrisonbliss]

Patrick I have just found your videos and I just wanted to say you are totally amazing for doing this, I can imagine you are in a way higher level of maths than this and you're just doing this for your fellow human beings. Just wanted to let you know your work is appreciated and you must be seriously handsome. Thank you!

[@patrickjmt]

my pleasure, glad you like the videos :)

[@aco8081]

A couple days ago if you asked me how I felt about my upcoming calc2 exam I would tell you that I felt like hundreds of escaped dementors from Azkaban had sucked every ounce of hope and happiness I had from my lifeless body. Today, after spending hours watching your videos, I can see the light again! Thank you so very much for being my patronus! I don't know how I would have gotten through this without you!

[@mugipoptarts]

Thank you so much for taking the time to do this. It means a lot! :)

[@MiggyCon]

gosh thank you! your videos are way better than long hours of lecture

[@1111mahima]

you are sent straight from heaven for us struggling college students.

[@aksmy3]

I have to write this comment, otherwise I'd feel guilty It's 1:15am ...and i have been watching and doing my homework since 1:00pm. The one thing that I love is that you make me hold on to calculus. I know that i'd be a slacker without you. I am so grateful and thankful for the knowledge you share. I will pray that you reach all your goals in life. - Indian student.

[@MrBlash93]

Thank you so much Patrick. I really appreciative all of your help.

[@patrickjmt]

i tried to get a part time job there a couple of years ago, but then never wrote back :) i have also tried contacting one of the resource centers there to help get my videos to UT students but again, no response :) good luck with your own writings!

[@surferboy198]

oh my god mate I wanna thank you so much!! you're the reason why i'm going to pass my exam maths on the end of this year!!!!!

[@emadmoha6605]

Update ?

[@coolguy209111]

got my final marks two days ago and calc was the highest! Thanks again & i'm sure I will be watching your videos for calc 2 and 3 as well

[@dcastleman1]

You have such an amazing gift of teaching calculus.

[@europeanbamf]

Thanks for the time you put into these Patrick

[@ShakarBradost]

3 years ago i came here to learn few integration techniques and now here i am for the reason again. Thank god for youtube and patrickJMT

[@ronniemonnie]

Hey patrick I'm about to write my final term test of the year next week, and if I get an A on this one, I'll have A's on all my tests this year, and it'll be thanks in (great) part to you. I don't wanna jynx it, but I really feel like I'm gonna get a 4.0 in this class, which would just be great because I despised calculus before, but your videos made me ENJOY math. I don't know if you're aware of how much you actually help people, but you're a life saver. Thanks.

[@divanshusagar9572]

Sir I can't tell you how happy I am after watching this video keep it up sir

[@JustOneGuy]

When 9 years old , 20 minutes video explains it better than months of college.

[@Toby_Gomez]

Amazing teacher, I've been watching since high school I'm going into Calc now , thanks man!

[@Plaq-gl7sy]

You have a gift for teaching and explaining things. You're very CLEAR!

[@ashaan586]

You taught me how to do my homework since school started! I gotta subscribe to you!

[@patrickjmt]

happy to help :) and yes, great researchers do not always make for great teachers! plus, having 200+ students in a lecture hall is never a good thing imo.

[@zeynepates8456]

Thank you so much Patrick, I understood all of the partial fractions. Now ; I can solve all my questions.

[@hawzhinfuad2519]

it is 2016 and u still helping us thank uuuu!!!!!

[@saif16900]

2018 :)

[@ballisticbuddha]

Thank you so much, I unfortunately missed the lecture on this topic, but this is a pretty good alternative. You're a saint.

[@kendallcarter3491]

Thanks for all the work you are doing to provided free and understandable videos to people. You are a life saver.

[@hexacross]

PatrickJMT, you are an absurdly good teacher. Calculus final in two hours; let's do this!

[@nithinnj]

i love all your vids helps me in all my hard math classes thanks

[@elnino0ooo]

Dear Mr. PatrickJMT, I'm from Saudi Arabia, I'm really regretful of the time u spend on youtube trying to help people you dont know, to me you cant imagine how you helped me in my engineering courses. One last thing, I promise one day I'll meet you with lots of gifts to you my man for your big help in my career study. Thanks!

[@vemo2474]

Yes, the video from 2006 really helping!

[@degr8est493]

Teachers these days just want to rush through material as fast as possible and leave students in their dust..

[@patrickjmt]

No, this is not at all what teachers want. However, when i taught there was a ton of material and I was forced to do that. I think the way math is approached in USA is just terrible though

[@aliyuksel9266]

+patrickJMT Agreed..it feels like i just learn to follow steps..and don't realise what im actually doing while solving problems

[@titosamuel7397]

why cant you just go on and show how to solve it ?

[@paul2413]

It's not the teachers fault. You're supposed to spend your own time going over it. Teachers have a lot of content to cover so they have to rush. If they don't then I guarantee YOU would be the same person going "The teachers never taught us any of this!" in the exam.

[@RoninSama.official]

Thank you so much for this. I now completely understand when to put those Ax+B's etc. Thank you!

[@MisterItchy]

I have an awesome professor but a lousy memory ... thank you very much for the videos about all the things I 'learned' in pre-calc and algebra!

[@Bakugantsuvai1]

Patrick, I love your "power line" puns a good analogy to remember that crucial step.

[@padraiga]

Thanks for taking the time to do these.

[@defendurrootz]

who wouldve thought that a geek could be so smart... keep up the good work patrick

[@kfespirituu]

thank you so much for your videos! im in calc II and you explain it better than my prof

[@tallyferguson7315]

Thank you so much for the time you take to do these videos. My calc mark and I both deeply appreciate it.

[@eday00]

One day, I will build structures. I intend to build many of them. Each one will be safer because of you. I'm not sure what you get out of helping us, but I hope it blows your socks off.

[@patrickjmt]

@otownfever good luck on the exam!

[@ashkansnake]

This made no sense without being a youtube video, thank you

[@adrianputra4934]

Mannn!! YOU ARE AWESOME..!! I had been struggling in this problem.!! NOW IT'S SOLVED!! Thanks dude !!

[@kiptoocollins8430]

Indeed am going to pass my Cal.2 again this sem like last semester,,, I didn't get supplementary exam because of your good video explanation,, thanks much

[@annieluvdogs]

thank you so much for this! I missed the lecture because I had AP testing, and I havea test on this next week.

[@tjerriam]

thanks you patrick you must be my tutor man..your awesome! good luck to my final exam later this video really helps me alot! =)

[@JoseBelen1]

Partial Fractions made easy!!!! well at least in this video... On to the next! Thanks, Patrick!

[@Chavways]

You should be the one earning $100000 a year teaching maths instead of lecturers who haven't a clue. I've learned more in an hour watching your videos than I have in 6 weeks of maths lectures.

[@WickedChild95]

Totally awesome videos, very easy to understand and excellent example equations!

[@kimimaru4411]

Great explanation, I never again had problems with these integrals after this :D

[@chechennyboiiy]

at 18:03, why is x^2 linear, and he puts a constant B instead of BX+C?

[@user-pf3vz3rd9h]

he said when the factors are quadratic, it was (x)^2 so the function was squared not the factor.. thats what im guessing is the reason he considered it linear

[@ericohman]

+chechennyboiiy I was also confused but then I had a look at 9:00 again and I guess (yes, just guessing) that one could think that the x^2 at 18:03 is linear because it would be the same as (x+0)^2 where as something like (x^2+3) is not linear and therefore needs Ax+B

[@abaundwal]

Chenny It looks quadratic but it's actually reducible into linear factors x*x. That's why..

[@Wastelander1972]

Precal make up test on PFD tomorrow. You rock, man.

[@tanshikohli6730]

it has really helped me clearing my us high school exams

[@dd92727]

Buy a text for high schools " Core Maths for A-Level 3rd Edition - L. Bostock, S. Chandler" you can find one on amazon real cheap under $10. Partial fractions are taught in high school in Europe and Africa under the Cambridge exams. Its a great text and it covers most of the college math done here in USA. American Math textbooks are badly written.

[@patrickjmt]

they are also insanely expensive

[@SpnFan04]

you explain better than my prof and make it seem less scary! thanks so much!

[@dannyphan4922]

I just love how he's left handed.

[@RobStephfanfver]

I hate Partial Fractions! I never could get the coefficients or know how to break up the thing in the first place. These vids are a major help. Thank you!

[@alexminser1482]

Finally a video that actually explains how to do this. Thanks patrick.

[@Darkoriangio]

you're a big help thanks mr.patrick

[@BoredMattable]

Weirdly enough I also go to UT and have to use your videos to understand most of the new concepts, I feel like its very hit or miss with our teachers here; despite our high rankings. Anyway, I'd be failing Calculus without you so thanks, keep it up!

[@gilma4328]

Thank you so much, this is perfect explanation that I never find in the book. I appreciate it.

[@patrickjmt]

happy to help :)

[@HellaPerformance]

You should put integration somewhere in the title or the description. I was turned away from this video a few times before actually watching it because I assumed it was just partial fraction decomposition without the calculus. Other than that, excellent video! Thank you so much!

[@Nixilius]

Thanks a lot for this, you explain this much better than my uni teacher