Polynomial division | Polynomial and rational functions | Algebra II | Khan Academy

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  • Опубликовано: 4 фев 2025

Комментарии • 502

  • @Echo93611
    @Echo93611 13 лет назад +988

    I just want to thank the internet for letting me sleep during an hour of algebra 2, then spend 10 minutes on youtube and understand the subject perfectly.

    • @tinaandersen3270
      @tinaandersen3270 6 лет назад +6

      School is important

    • @aristarchinski272
      @aristarchinski272 5 лет назад +30

      @@tinaandersen3270 Un*

    • @woutergrob8587
      @woutergrob8587 5 лет назад +75

      @@aristarchinski272 If that's your standpoint you're either gotta known how to use your charisma to make trades (car dealership, etc) or you better remember I like my cheeseburgers with extra cheese.

    • @crazycatlady7326
      @crazycatlady7326 4 года назад +2

      I'm learning this in algebra 1...lol

    • @gokublack3231
      @gokublack3231 4 года назад +17

      Wonder how this guy is doing now since 8 years have passed

  • @elinag5743
    @elinag5743 8 лет назад +233

    thank you! my math classes never taught this, yet these problems appear on tests. the education system sets us up for failure, but khan academy is our saving grace.

    • @elinag5743
      @elinag5743 8 лет назад

      Alberto Garcia why do you think that?

    • @elinag5743
      @elinag5743 8 лет назад +6

      Alberto Garcia fair argument. Sal can't really change his voice though. And the slow teaching helps a lot of people.

    • @jaskaransingh6440
      @jaskaransingh6440 8 лет назад +33

      his voice is good and never irritating

    • @elinag5743
      @elinag5743 8 лет назад +13

      Jaskaran Singh i agree. but everyone has different preferences. even if his voice did irritate me, I'd still get over it and appreciate the video for its content

    • @graphene1487
      @graphene1487 5 лет назад +3

      @Alberto Garcia you suck big. Give the guy a break.

  • @shellybee5477
    @shellybee5477 10 лет назад +136

    Math has always scared me because I've always found it so intimidating. But whenever I watch Sal's videos he has a way of making math seem fun and exciting. A rare gift indeed. My anxiety seems to disappear as he so calmly explains the steps.
    Thank you for making math fascinating, sal! Your videos have changed my entire perspective on math.

  • @peircingblueeyes
    @peircingblueeyes 11 лет назад +441

    God bless Khan Academy..

  • @Bonbonenata
    @Bonbonenata 10 лет назад +291

    I'm gonna thank you in my graduation speech!!

    • @Lune___.
      @Lune___. 5 лет назад +17

      @Edwin Favela 5 years later lmao

    • @TheInfernoGamer10
      @TheInfernoGamer10 4 года назад +6

      Oi we wanna hear ya speech

    • @eylulvv
      @eylulvv 4 года назад +2

      Hellooooo

    • @Bonbonenata
      @Bonbonenata 4 года назад +46

      Can't believe someone replied 5 years later :o Turns out I'm not smart enough to have a graduation speech 😅 but I did pass all my math exams :D

    • @samuelrasquinha6712
      @samuelrasquinha6712 4 года назад +3

      @@Bonbonenata yay!

  • @princessalexander1349
    @princessalexander1349 6 лет назад +245

    "lets do another one of these. They're kind of fun!" ~rewinds video to make sure I heard that right~

  • @roflsteph
    @roflsteph 10 лет назад +23

    I've always strugged so much in math and these videos are saving my GPA! I learn so much more from these videos than in the actual class.

  • @thestig560
    @thestig560 5 лет назад +8

    3:20 thank you for clarifying the minus thing, it made all the difference!

  • @movingwall1
    @movingwall1 11 лет назад +38

    My teacher spent three lessons explaining this. And I couldn't understand it. After 12 minutes of you explaining it I totally understood.

  • @TopsShots
    @TopsShots 8 лет назад +153

    HOLY SHIT I FUCKING LEARNED HOW TO DO THIS IN A 12 MINUTE VIDEO BUT COULDN'T FOR 2 WEEKS IN A 40 MINUTE CLASS

  • @hollyemerson5973
    @hollyemerson5973 12 лет назад +5

    I always find myself searching your videos after my math teacher's ATTEMPT at showing me. I don't know where I would be right now without you and your videos. So, thank you for making my life a little easier.
    sincerely,
    confused math studentttttttt

  • @zdrasbuytye
    @zdrasbuytye 10 лет назад +65

    OMG I was struggling like one hour with one problem like the one that you showed in the last minutes . After that, I finished my problem in one minute. You're really awesome.

  • @djeroid2000
    @djeroid2000 10 лет назад +7

    THANK YOU BASED SALMAN KHAN!
    For the longest time since high school, I had extreme trouble dealing with polynomial long division and once it again, it came back in Differential Equations (when dealing with partial fractions). Your video finally gave me a full understanding of how to do this! Thanks again! :)

  • @marokay3269
    @marokay3269 11 лет назад +3

    What I think about in math class "I'm gonna watch a khan academy video in this" these vids are a great blessing for all of us

  • @lance_nickel
    @lance_nickel 4 года назад +3

    This man is a true hero. Publishing all this great knowledge, for free. Man's a saint.

  • @Katamaricolby
    @Katamaricolby 9 лет назад +57

    I was never good with long division... :/ So many steps to remember, at least for me.

    • @nii_san1201
      @nii_san1201 7 лет назад +1

      SAME BRO, SAME

    • @aneesak-ar-im3869
      @aneesak-ar-im3869 6 лет назад +1

      Thought I was the only one who just never remembered how to do this...

    • @rotopope
      @rotopope 5 лет назад +4

      It isn’t really an intuitive process.

  • @FinalCutVideography
    @FinalCutVideography 9 лет назад +333

    still don't get it im doing it a different way hahahahah *laughs then cries*

    • @Zohirul-Jewel
      @Zohirul-Jewel 8 лет назад +12

      His teaching methods aren't always the best

    • @maiamaya381
      @maiamaya381 7 лет назад +18

      But generally they could help. There is no perfect method of teaching so it's okay if you don't understand...

    • @RicardoSanchez-hl3qy
      @RicardoSanchez-hl3qy 5 лет назад +1

      Wow

    • @peanutbudderr5352
      @peanutbudderr5352 4 года назад +1

      @@maiamaya381 i agree

    • @ChiccinTendies
      @ChiccinTendies 4 года назад +9

      The best thing to do is to take a deep breath and slow it down. Most times people freak out and panic, preventing themselves from doing something that's well within their capability.

  • @DoubleCrossedPaths
    @DoubleCrossedPaths 10 лет назад +4

    As someone in a college Math 42 class taught by a teacher that moves through material quickly and offers little help or mercy, these videos and the content on the Khan Academy website may be enough to turn the disaster that was the first 3 tests in the class around. Very glad I was referred to this.

  • @groupgreatness1469
    @groupgreatness1469 5 лет назад +1

    You have changed my life

  • @jetpackhamster8662
    @jetpackhamster8662 6 лет назад +1

    This guy makes math way easier.

  • @NateNate60
    @NateNate60 7 лет назад +3

    3:57 "6 minus 0 is nothing" Makes total sense

  • @alarmgoesding
    @alarmgoesding Год назад +1

    2 days from a calculus exam and I learned long division in 5 minutes after not having done it in over 10 years. Sal is amazing as always.

  • @ARKILLER95
    @ARKILLER95 12 лет назад

    This is magic. My teacher, friends and maths tutor couldn't explain this too me with me understanding. But when with your video I learnt how to do it half way through like 6minutes! Praise you Mr.Khan

  • @elitesoccer96
    @elitesoccer96 12 лет назад +1

    Who needs school when we have khan academy. We should replace math teachers with Khan Academy videos.

  • @shubhkedia259
    @shubhkedia259 2 года назад +1

    Really helps! I used to despise algebraic long divisions but now I go into my class and do the same sums I previously used to hate rather than complete my homework.

  • @biwwi100
    @biwwi100 11 лет назад +1

    This actually blew my mind. Nobody taught me this!

  • @lorainecastro5677
    @lorainecastro5677 10 лет назад +2

    This video is such a big help for our quiz tomorrow, thanks!

  • @LandDestroyer
    @LandDestroyer 6 лет назад +1

    It has been 15 years since I've done algebraic long division and this video helped me remember it. Thanks!

  • @gamerslife5375
    @gamerslife5375 3 года назад +1

    THANK YOU SOOOOOOOO MUCH I HAVE MY EXAM IN A WEEK AND THIS WAS THE ONLY CONCEPT NOT CLEAR TO ME YOU MADE IT FUN AND EASY THANKK U

  • @ajitated1211
    @ajitated1211 8 лет назад

    I do online schooling, and a lot of times the assignments (at least the math ones) come with somebody doing a few examples, but the one I'm on right now didn't. I'm a visual learner, where I have to have somebody show me how to do something instead of just reading it. So, these videos have really helped me learn this when my assignments couldn't.

  • @dularar8934
    @dularar8934 5 лет назад +1

    Really helps

  • @FaceSTAB411
    @FaceSTAB411 11 лет назад +2

    Hard to understand, hard to remember, but once they're there it's all good.
    Thanks dude. 'Preciate it.

  • @stephenfoster7465
    @stephenfoster7465 7 лет назад +1

    THIS GUY JUST ANSWERED EVERY ONE OF MY QUESTIONS

  • @shaunceyy1851
    @shaunceyy1851 6 лет назад +1

    Thank you very much Khan Academy! My Math exam is on Wednesday and this Video has really helped me out A LOT! ThAnks So mUCH!

  • @nathanaelfoo
    @nathanaelfoo 12 лет назад

    Within 12 minutes,I have mastered division of polynomial.Mr Khan,U ARE AMAZING!!!THANK YOU.

  • @balsyitlog
    @balsyitlog 11 лет назад +1

    Thank you. Very helpful. I forgot these things and now I need em again for entrance exams. Wish me luck! God bless to you. :)

  • @Jixzah
    @Jixzah 8 лет назад +28

    Thanks man I have a test tomorrow and I can't learn from my teacher. This is still frustrating though

    • @h_67tyherwegoagain86
      @h_67tyherwegoagain86 6 лет назад +2

      So.. How did it go?

    • @danielj.g.1328
      @danielj.g.1328 6 лет назад +2

      We want to know how it went

    • @gkmwheelspin1207
      @gkmwheelspin1207 5 лет назад +2

      Think about how insignificant that test was compared to now.... Either way, I hope you did great

    • @bricklord5017
      @bricklord5017 3 года назад

      Lol I also have a test tomorrow, and I kinda need to get my math grade up for this quarter so that it will bring up my semester grade which will maintain my year grade which combined with a dew other years will be viewed by colleges and majorly discount the price if I get a scholarship, and if I dont I may not be able to go to college or at least the one I want to go to which means I might not be able to fulfill my career :/ so no pressure

  • @mattt2684
    @mattt2684 7 лет назад +2

    Thank you SO MUCH for explaining this is a clear and concise manner.

  • @mattpowelluk1
    @mattpowelluk1 12 лет назад

    Studied Polynomial Division at college today and really did not understand it, after watching your video I understand it completely and actually enjoy solving the equations. Thank you

  • @TeamTTToxic
    @TeamTTToxic 5 лет назад

    Took me 30 min to try and work this out with worked examples, no use. This video has been extremely helpful, thank you.

  • @jonathanbyrdmusic
    @jonathanbyrdmusic Год назад

    I can't imagine getting an A in precalc without Khan Academy.

  • @clemsoncutie2014
    @clemsoncutie2014 12 лет назад +1

    Thank you so much for your free math lessons! I would probably be failing calculus right now if it weren't for you!

  • @ChernobylPizza
    @ChernobylPizza 10 лет назад +3

    Describing it like long division was really confusing to me. Haven't done long division since 4th grade so I you lost me there. But when I think of it my own intuitive way it makes sense and I was able to do the problem in seconds.

  • @megharanjit6117
    @megharanjit6117 4 года назад

    This is so much better than Biju's. I have that app in my phone and still I am looking at Khan academy to clear my doubts.
    Thank you Khan academy ❤️

  • @Psychadellichick
    @Psychadellichick 13 лет назад +1

    I'm legit crying right now. I'm going to pass my math class now. Thank you SO much, Sal.

  • @scottmcknight8875
    @scottmcknight8875 10 лет назад +2

    Honestly saved my test grade. Thank you!

  • @cleverdamn
    @cleverdamn 3 года назад

    Khans been helping me from the last year's of highschool to the last years of my physics bachelor

  • @kasus2gakjelas
    @kasus2gakjelas 6 лет назад

    Hi Mr. Khan! I just want to tell you that I got a 100% for my test. I was missing out in class by a lot and I watched your videos and got perfect for my second quiz of the year. I got a 10% on the first test, but after watching your videos I got a perfect score on the second one! THANK YOU SO MUCH... YOU'RE THE BEST!!!!!!!!!!!!!!!!!

  • @kobragaming7078
    @kobragaming7078 3 года назад +1

    I got a test rn and this is helping me alotw

  • @Crux161
    @Crux161 10 лет назад +2

    this was an excellent video, the last example was JUST what I needed... thanks for helping me to brush up for midterms! xD

  • @madi2004
    @madi2004 4 года назад

    I have a test on this in two days and absolutely understood zero of it in class. Thank you so much!

  • @FrozenTint
    @FrozenTint 3 года назад +1

    after 10 years ...i'm now watching the video in 2021 and I can't imagine how helpful it is

  • @sverenagain
    @sverenagain 3 года назад

    thanks for explaning in 12 minutes what my teacher couldnt in an hour!

  • @Hughesgr155
    @Hughesgr155 13 лет назад +1

    Thank you, you helped my make sense of a homework assignment (x+a, with x being squared).

  • @ragnarrocksoft9096
    @ragnarrocksoft9096 4 года назад +1

    Thanks a lot for saving my maths grade this semester

  • @IvanGaro
    @IvanGaro 11 лет назад +2

    I love Khan Academy, and my math class is crazy hard! I can't take it! Like when are we gonna use this in real life?

  • @brandonankumah280
    @brandonankumah280 6 лет назад +2

    OMG I watched this video many times before I understood. THANKS SOOO MUCH

  • @s9m8123
    @s9m8123 12 лет назад

    Thank you so much for providing your math lessons free of charge! They are helpful to so many people, including myself, and I think I can speak for us all when I saw that they are wonderful!

  • @josesaucedo1073
    @josesaucedo1073 10 лет назад

    YOU ARE THE SAVIOR OF MY FINALS. I don't know why I didn't understood this before. Takes me a minute now, thx

  • @mandeep3.14
    @mandeep3.14 6 лет назад +2

    Mind-blown. It really helped that you showed it from the very beginning in simpler terms and then show what you found after by putting it back into the original, especially cos i was commmppllleetteelllyyy unaware of that division method until today...i just put the remainders next to the digit (which i tried to apply to this and failed miserably) xD
    I spent a good portion of today in confusion and mild despair at the first bloody chapter!, feel a bit better now that i've understood this v_v'

  • @cadence9308
    @cadence9308 13 лет назад +1

    filling those gaps. Thanks Sal!

  • @achrafhm2905
    @achrafhm2905 9 лет назад +1

    MY GOD I SWARE I HAVE LEARNT THIS FROM YOU THAN FROM MY TEACHER AT LEAST YOU SHOW US EVERY THING WE DONT KNOW MAN I THINK I WILL GET IN 90S THIS YEAR BECAUSE OF YOU SALMAN KHAN I WILL TELL EVERY FRIEND OF ME ABOUT YOUR CHANNEL

  • @lowclientfps9640
    @lowclientfps9640 4 года назад

    That feeling of relief of finally understanding the lesson that was taught by your teacher for A WEEK

  • @intenseleaf
    @intenseleaf 11 лет назад

    The thing about math for most people is that you won't. The main purpose of teaching so much math in school is because it teaches you logical problem solving, which is something that will REALLY benefit you in the long-run. Plus, colleges love someone who's done well at math :)

  • @AllTrickss
    @AllTrickss 6 лет назад

    Your 12 min video explains this more clearer than my teacher talking about it for 30 min

  • @ShortScenesForYou
    @ShortScenesForYou 10 лет назад +3

    This saved my test grade! thank you

  • @KhaxiChi
    @KhaxiChi 5 лет назад

    wow...I THANK YOU VERY MUCH!.....i won't pass my 3rd quarter exam if it wasn't for this!...I missed my lesson due to the event i was in to my school...but...this video make me catch up to where my teacher left us!...THANK YOU VERY MUCH!

  • @kickstarts2910
    @kickstarts2910 5 лет назад +5

    Let's do another one of these
    *It's kind of fun*

    • @bricklord5017
      @bricklord5017 3 года назад

      Also him later:
      I hope u found this as fun as I did

  • @StrictlyMediocre
    @StrictlyMediocre 9 лет назад +6

    Yo this makes so much sense! Thanks so much! I thought I was going to fail my test tomorrow for a second.

  • @TheBestOfPKA
    @TheBestOfPKA 12 лет назад

    You are a saint for my online class. Thank you.

  • @Merthalophor
    @Merthalophor 4 года назад

    This is brilliant. The only thing I'd critique is the expression that "x goes zero times into four" at 4:32, which is not actually the reason to stop there, besides the fact that it's not true (x goes exactly 4/x times into 4) . The problem is not that the algorithm doesn't "work" anymore, it would still produce accurate results even if the narrator continued. The problem is only that from that point onward, the algorithm isn't simplifying terms anymore, it makes them more complicated. This is why we stop there and just write "4 / (x + 1)".

  • @kieudang4693
    @kieudang4693 11 лет назад +1

    Thank you :) Your videos has helped me with my Algebra class tremendously

  • @MultiClinton1234
    @MultiClinton1234 12 лет назад

    thankxx a lot.i wish u were my teacher.u make it look so easy.
    you are the BEST!

  • @group1896
    @group1896 6 лет назад

    thank goodness for videos like this. I forgot about this topic and this is my go-to channel from now on.

  • @AkshajSai-rt5xe
    @AkshajSai-rt5xe 6 месяцев назад

    man you're such a blessing to the world!

  • @MissLittleangel101
    @MissLittleangel101 8 лет назад +2

    This is really good i think i'll pass my placement test cuz of you thank you so much :)

  • @hamtaru
    @hamtaru 7 лет назад

    I recommend trying to solve the equations yourself after the first one if you can't get it right check what you forgot to do by continuing to watch the video. It helped me and I got the method in the first watch! 😁

  • @soursid300
    @soursid300 7 лет назад

    Wow you are pretty much better than any teacher!!

  • @mrugankbelsare
    @mrugankbelsare 10 лет назад

    you simply make it easy to learn maths!!!!!!!!!!!!!!!!!!!.

  • @jk97531jk
    @jk97531jk 11 лет назад

    Thanks! I kinda understood it before and I think I've got it now. Thanks! (again)

  • @ReemaAman-j5g
    @ReemaAman-j5g 2 месяца назад

    The best teacher in the world 🌎 🎉

  • @bril5842
    @bril5842 6 лет назад +1

    This really helped me in my homework because i was having trouble with it and my teacher explained it weirdly

  • @Ananyagarg09
    @Ananyagarg09 2 года назад

    Thank you so much I was preparing for my exams and I just couldn't understand how to divide algebraic expression and now I understand and I find it easy thanks a lot

  • @Hagarvlogs
    @Hagarvlogs 8 лет назад +1

    thats so helpful!! thank you 😭😭

  • @Scoutrider127
    @Scoutrider127 11 лет назад

    My head is hurting too much for me to be happy that I can finally do these problems in my homwework,

  • @TheNachodood
    @TheNachodood 12 лет назад +1

    Wow you're great! Thanks!

  • @Alonelyzealot
    @Alonelyzealot 12 лет назад

    usually you could just express it in that form as a fraction. if your teacher is picky about it, you would use it as a decimal. thats how i learnt to do it.

  • @juanx750
    @juanx750 12 лет назад

    Thank You So Much. my algebra teacher does not know how to explain this at all

  • @call1800jess
    @call1800jess 12 лет назад +2

    I just wanna say that I discovered this in Time magazine. Its really awesome!!! :)

  • @actuary32174
    @actuary32174 12 лет назад

    There is a technique from Vedic Math called "Division on the Flag" that allows you to divide any degree polynomial by any other polynomial and write the answer directly in about 1/10th of the time.

  • @christianjackson1806
    @christianjackson1806 3 года назад

    As time goes on and I learn more and more Algebra the stuff I so on boards in movies that seem so complicated don't seem as complicated anymore.

  • @arhamimran1382
    @arhamimran1382 4 года назад

    Sal you're a life saver. Period

  • @almostmybedtime
    @almostmybedtime 5 лет назад +1

    thanks sam, it was very helpful!!

  • @AnilZonderPunt
    @AnilZonderPunt 13 лет назад

    Thank you very much for your time and for sharing your knowledge. Divisions were always a bit blurry for me, you really helped!

  • @MrToolz
    @MrToolz 14 лет назад +1

    Hopefully you found that as fun as I did, lool
    great vids man, keep up the good work :)

  • @firefly1152
    @firefly1152 10 лет назад +1

    thank you very much! your videos are so easy to understand :)

  • @Poorvika17
    @Poorvika17 3 года назад

    Ur really helping me khan sir
    Hats off to uuuuu

  • @mustangsally2048
    @mustangsally2048 10 лет назад

    Thanks your the best teacher I've ever had at math

  • @silasfoley2971
    @silasfoley2971 6 лет назад

    This method worked very well!

  • @ShannonMarie543
    @ShannonMarie543 11 лет назад

    your voice is so cool. It makes maths cool