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

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  • เผยแพร่เมื่อ 2 พ.ย. 2024

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  • @Echo93611
    @Echo93611 13 ปีที่แล้ว +969

    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 ปีที่แล้ว +6

      School is important

    • @aristarchinski272
      @aristarchinski272 5 ปีที่แล้ว +31

      @@tinaandersen3270 Un*

    • @woutergrob8587
      @woutergrob8587 5 ปีที่แล้ว +74

      @@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 ปีที่แล้ว +2

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

    • @gokublack3231
      @gokublack3231 4 ปีที่แล้ว +17

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

  • @elinag5743
    @elinag5743 7 ปีที่แล้ว +232

    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 7 ปีที่แล้ว

      Alberto Garcia why do you think that?

    • @elinag5743
      @elinag5743 7 ปีที่แล้ว +6

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

    • @jaskaransingh6440
      @jaskaransingh6440 7 ปีที่แล้ว +33

      his voice is good and never irritating

    • @elinag5743
      @elinag5743 7 ปีที่แล้ว +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 ปีที่แล้ว +3

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

  • @Bonbonenata
    @Bonbonenata 10 ปีที่แล้ว +290

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

    • @Lune___.
      @Lune___. 4 ปีที่แล้ว +17

      @Edwin Favela 5 years later lmao

    • @TheInfernoGamer10
      @TheInfernoGamer10 4 ปีที่แล้ว +6

      Oi we wanna hear ya speech

    • @eylulvv
      @eylulvv 4 ปีที่แล้ว +2

      Hellooooo

    • @Bonbonenata
      @Bonbonenata 4 ปีที่แล้ว +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 ปีที่แล้ว +3

      @@Bonbonenata yay!

  • @peircingblueeyes
    @peircingblueeyes 10 ปีที่แล้ว +441

    God bless Khan Academy..

  • @shellybee5477
    @shellybee5477 10 ปีที่แล้ว +135

    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.

    • @cheese-y1y
      @cheese-y1y 2 ปีที่แล้ว

      How's life now?

    • @mrbagginz5963
      @mrbagginz5963 9 หลายเดือนก่อน

      I bet it is good

  • @princessalexander1349
    @princessalexander1349 5 ปีที่แล้ว +245

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

  • @roflsteph
    @roflsteph 10 ปีที่แล้ว +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.

  • @TopsShots
    @TopsShots 8 ปีที่แล้ว +151

    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

    • @darknotez7170
      @darknotez7170 8 ปีที่แล้ว +12

      Forreal thats exactly how i feel. My teacher blows at teaching.

    • @Scyphersoarocx
      @Scyphersoarocx 8 ปีที่แล้ว +1

      preach it bro

    • @Scyphersoarocx
      @Scyphersoarocx 8 ปีที่แล้ว +4

      #TheAmericanEducationSystem

    • @vicwang271
      @vicwang271 8 ปีที่แล้ว +3

      Scyphersoarocx ikr

    • @vicwang271
      @vicwang271 8 ปีที่แล้ว

      Scyphersoarocx ikr

  • @movingwall1
    @movingwall1 11 ปีที่แล้ว +38

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

  • @FinalCutVideography
    @FinalCutVideography 9 ปีที่แล้ว +335

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

    • @Zohirul-Jewel
      @Zohirul-Jewel 7 ปีที่แล้ว +12

      His teaching methods aren't always the best

    • @maiamaya381
      @maiamaya381 6 ปีที่แล้ว +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 4 ปีที่แล้ว +1

      Wow

    • @peanutbudderr5352
      @peanutbudderr5352 4 ปีที่แล้ว +1

      @@maiamaya381 i agree

    • @ChiccinTendies
      @ChiccinTendies 4 ปีที่แล้ว +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.

  • @zdrasbuytye
    @zdrasbuytye 10 ปีที่แล้ว +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.

  • @Katamaricolby
    @Katamaricolby 8 ปีที่แล้ว +57

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

    • @nii_san1201
      @nii_san1201 7 ปีที่แล้ว +1

      SAME BRO, SAME

    • @aneesak-ar-im3869
      @aneesak-ar-im3869 5 ปีที่แล้ว +1

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

    • @rotopope
      @rotopope 5 ปีที่แล้ว +4

      It isn’t really an intuitive process.

  • @djeroid2000
    @djeroid2000 9 ปีที่แล้ว +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! :)

  • @thestig560
    @thestig560 5 ปีที่แล้ว +8

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

  • @marokay3269
    @marokay3269 11 ปีที่แล้ว +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 ปีที่แล้ว +3

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

  • @hollyemerson5973
    @hollyemerson5973 11 ปีที่แล้ว +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

  • @DoubleCrossedPaths
    @DoubleCrossedPaths 10 ปีที่แล้ว +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.

  • @NateNate60
    @NateNate60 7 ปีที่แล้ว +3

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

  • @jetpackhamster8662
    @jetpackhamster8662 6 ปีที่แล้ว +1

    This guy makes math way easier.

  • @Jixzah
    @Jixzah 8 ปีที่แล้ว +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 ปีที่แล้ว +2

      So.. How did it go?

    • @danielj.g.1328
      @danielj.g.1328 5 ปีที่แล้ว +2

      We want to know how it went

    • @gkmwheelspin1207
      @gkmwheelspin1207 5 ปีที่แล้ว +2

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

    • @bricklord5017
      @bricklord5017 2 ปีที่แล้ว

      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

  • @alarmgoesding
    @alarmgoesding ปีที่แล้ว +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.

  • @shubhkedia259
    @shubhkedia259 2 ปีที่แล้ว +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.

  • @lorainecastro5677
    @lorainecastro5677 9 ปีที่แล้ว +2

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

  • @ChernobylPizza
    @ChernobylPizza 9 ปีที่แล้ว +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.

  • @shaunceyy1851
    @shaunceyy1851 6 ปีที่แล้ว +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!

  • @mattt2684
    @mattt2684 6 ปีที่แล้ว +2

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

  • @LandDestroyer
    @LandDestroyer 5 ปีที่แล้ว +1

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

  • @ajitated1211
    @ajitated1211 8 ปีที่แล้ว

    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.

  • @jaredgrant1067
    @jaredgrant1067 5 ปีที่แล้ว +26

    "hopefully you found that as fun as I did"

  • @groupgreatness1469
    @groupgreatness1469 5 ปีที่แล้ว +1

    You have changed my life

  • @ARKILLER95
    @ARKILLER95 11 ปีที่แล้ว

    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

  • @FaceSTAB411
    @FaceSTAB411 11 ปีที่แล้ว +2

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

  • @kasus2gakjelas
    @kasus2gakjelas 6 ปีที่แล้ว

    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!!!!!!!!!!!!!!!!!

  • @Crux161
    @Crux161 10 ปีที่แล้ว +2

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

  • @biwwi100
    @biwwi100 11 ปีที่แล้ว +1

    This actually blew my mind. Nobody taught me this!

  • @mandeep3.14
    @mandeep3.14 6 ปีที่แล้ว +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'

  • @TeamTTToxic
    @TeamTTToxic 5 ปีที่แล้ว

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

  • @kickstarts2910
    @kickstarts2910 5 ปีที่แล้ว +5

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

    • @bricklord5017
      @bricklord5017 2 ปีที่แล้ว

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

  • @kieudang4693
    @kieudang4693 10 ปีที่แล้ว +1

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

  • @brandonankumah280
    @brandonankumah280 5 ปีที่แล้ว +2

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

  • @gamerslife5375
    @gamerslife5375 2 ปีที่แล้ว +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

  • @wolfierex
    @wolfierex 8 ปีที่แล้ว +6

    I really enjoyed this video, and I thank Khan Academy for their help!

  • @Psychadellichick
    @Psychadellichick 13 ปีที่แล้ว +1

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

  • @megharanjit6117
    @megharanjit6117 3 ปีที่แล้ว

    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 ❤️

  • @StrictlyMediocre
    @StrictlyMediocre 9 ปีที่แล้ว +6

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

  • @stephenfoster7465
    @stephenfoster7465 7 ปีที่แล้ว +1

    THIS GUY JUST ANSWERED EVERY ONE OF MY QUESTIONS

  • @scottmcknight8875
    @scottmcknight8875 9 ปีที่แล้ว +2

    Honestly saved my test grade. Thank you!

  • @s9m8123
    @s9m8123 12 ปีที่แล้ว

    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!

  • @AllTrickss
    @AllTrickss 6 ปีที่แล้ว

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

  • @clemsoncutie2014
    @clemsoncutie2014 12 ปีที่แล้ว +1

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

  • @josesaucedo1073
    @josesaucedo1073 9 ปีที่แล้ว

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

  • @FrozenTint
    @FrozenTint 3 ปีที่แล้ว +1

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

  • @KhaxiChi
    @KhaxiChi 4 ปีที่แล้ว

    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!

  • @group1896
    @group1896 6 ปีที่แล้ว

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

  • @sverenagain
    @sverenagain 3 ปีที่แล้ว

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

  • @nathanaelfoo
    @nathanaelfoo 11 ปีที่แล้ว

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

  • @intenseleaf
    @intenseleaf 11 ปีที่แล้ว

    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 :)

  • @ShortScenesForYou
    @ShortScenesForYou 10 ปีที่แล้ว +3

    This saved my test grade! thank you

  • @balsyitlog
    @balsyitlog 11 ปีที่แล้ว +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. :)

  • @IvanGaro
    @IvanGaro 11 ปีที่แล้ว +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?

    • @Keemstar-ss7nu
      @Keemstar-ss7nu 3 ปีที่แล้ว

      did u use it 8 years later

    • @bricklord5017
      @bricklord5017 2 ปีที่แล้ว

      COME ON, THE PEOPLE NEED ANSWERS!!!!!!

  • @lowclientfps9640
    @lowclientfps9640 3 ปีที่แล้ว

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

  • @madi2004
    @madi2004 4 ปีที่แล้ว

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

  • @cleverdamn
    @cleverdamn 3 ปีที่แล้ว

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

  • @achrafhm2905
    @achrafhm2905 9 ปีที่แล้ว +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

  • @elitesoccer96
    @elitesoccer96 11 ปีที่แล้ว +1

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

  • @AkshajSai-rt5xe
    @AkshajSai-rt5xe 3 หลายเดือนก่อน

    man you're such a blessing to the world!

  • @mattpowelluk1
    @mattpowelluk1 12 ปีที่แล้ว

    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

  • @MissLittleangel101
    @MissLittleangel101 8 ปีที่แล้ว +2

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

  • @jonathanbyrdmusic
    @jonathanbyrdmusic ปีที่แล้ว

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

  • @dularar8934
    @dularar8934 5 ปีที่แล้ว +1

    Really helps

  • @bril5842
    @bril5842 5 ปีที่แล้ว +1

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

  • @Merthalophor
    @Merthalophor 4 ปีที่แล้ว

    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)".

  • @hamtaru
    @hamtaru 7 ปีที่แล้ว

    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! 😁

  • @Ananyagarg09
    @Ananyagarg09 2 ปีที่แล้ว

    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

  • @kobragaming7078
    @kobragaming7078 2 ปีที่แล้ว +1

    I got a test rn and this is helping me alotw

  • @cadence9308
    @cadence9308 13 ปีที่แล้ว +1

    filling those gaps. Thanks Sal!

  • @ragnarrocksoft9096
    @ragnarrocksoft9096 4 ปีที่แล้ว +1

    Thanks a lot for saving my maths grade this semester

  • @call1800jess
    @call1800jess 12 ปีที่แล้ว +2

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

  • @Hughesgr155
    @Hughesgr155 13 ปีที่แล้ว +1

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

  • @konozrashid887
    @konozrashid887 4 ปีที่แล้ว

    Thank you very much for helping me out. By the way, can you make a kind of research video on this long division and include the division of both polynomials and numbers? That way I would understand the true essence of division. And it would also make my logic regarding this polynomials' division more clear.

  • @austynchallis6525
    @austynchallis6525 11 ปีที่แล้ว +3

    Yup it was fun. It was so much fun, I literally pissed myself from all the laughing and smiling. -.-

  • @AnilZonderPunt
    @AnilZonderPunt 13 ปีที่แล้ว

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

  • @firefly1152
    @firefly1152 10 ปีที่แล้ว +1

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

  • @almostmybedtime
    @almostmybedtime 5 ปีที่แล้ว +1

    thanks sam, it was very helpful!!

  • @Rong0369
    @Rong0369 7 ปีที่แล้ว

    It give me extra knowledge and more confident to face any long division problem. If you don't believe me, ask me any questions from Division Algorithm for polynomial. I'm ready

  • @Lune___.
    @Lune___. 4 ปีที่แล้ว +5

    he really likes to talk about all his ex's

  • @MultiClinton1234
    @MultiClinton1234 12 ปีที่แล้ว

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

  • @MrToolz
    @MrToolz 13 ปีที่แล้ว +1

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

  • @christianjackson1806
    @christianjackson1806 3 ปีที่แล้ว

    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.

  • @actuary32174
    @actuary32174 11 ปีที่แล้ว

    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.

  • @josephrios7139
    @josephrios7139 6 ปีที่แล้ว

    In the last week example, when you divide the higher degree polynomial by the quadratic equation, why, when you multiply the 1 in, (x+1), with the 2 in, (3x-2), it the two a positive and not negative as illustrated.

  • @Scoutrider127
    @Scoutrider127 11 ปีที่แล้ว

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

  • @alexabulnaga6691
    @alexabulnaga6691 12 ปีที่แล้ว +15

    "They're kind of fun"
    -.-

  • @Poorvika17
    @Poorvika17 3 ปีที่แล้ว

    Ur really helping me khan sir
    Hats off to uuuuu

  • @insertnamhere568
    @insertnamhere568 10 ปีที่แล้ว +2

    thanks a bunch!!! i finally get this!!!!! :)

  • @Hagarvlogs
    @Hagarvlogs 8 ปีที่แล้ว +1

    thats so helpful!! thank you 😭😭

  • @soursid300
    @soursid300 6 ปีที่แล้ว

    Wow you are pretty much better than any teacher!!

  • @TheBestOfPKA
    @TheBestOfPKA 12 ปีที่แล้ว

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

  • @jk97531jk
    @jk97531jk 11 ปีที่แล้ว

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