Finding All Zeros of a Polynomial Function Using The Rational Zero Theorem

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  • เผยแพร่เมื่อ 5 ก.ย. 2024

ความคิดเห็น • 587

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  ปีที่แล้ว +27

    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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    • @user-xh5we2wi5z
      @user-xh5we2wi5z 5 หลายเดือนก่อน

      I enjoy your lecture

  • @norvin7410
    @norvin7410 3 ปีที่แล้ว +1773

    This guy is saving millions of students from failing. godbless this dude!

    • @rutii.a6428
      @rutii.a6428 2 ปีที่แล้ว +29

      Amen! He saved me too.

    • @roblominmus
      @roblominmus 2 ปีที่แล้ว +30

      I legit have a test on this topic tomorrow, he just saved my grades.

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      @absolute6422 2 ปีที่แล้ว +11

      He’s a literal god send

    • @mekdestsegaye9825
      @mekdestsegaye9825 2 ปีที่แล้ว +3

      Amen

    • @erikduzelljr
      @erikduzelljr ปีที่แล้ว +7

      Dude yeah. I'm taking online course and the explanations from professors suck. This guy explains simply and slowly so my dumbass can understand. Thank you!

  • @breadedlemon7067
    @breadedlemon7067 3 ปีที่แล้ว +513

    I like how he doesn’t edit out his mistakes nor does he retake his recordings, it always feels like he does these videos in one go

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    @xkt-jz9dx 4 ปีที่แล้ว +591

    Watched him from high school and now graduating with an associates all the way with him. Now it’s my turn to teach my little sister with his videos :)

  • @morriscallahan3549
    @morriscallahan3549 3 ปีที่แล้ว +164

    I just spent 2 hours in a lecture and had no idea what the rational zeros theorem was, but then I watched your video and it takes 10 seconds to learn it. thank you.

    • @user-xh5we2wi5z
      @user-xh5we2wi5z 5 หลายเดือนก่อน +1

      Mmmmm that's amazing, in 10 seconds

    • @abigaellejoseph8701
      @abigaellejoseph8701 2 หลายเดือนก่อน

      I literally just stopped showing up to lectures cause it feels like a waste of time. I don't learn anything

  • @Arthur-th4rm
    @Arthur-th4rm 5 ปีที่แล้ว +238

    As someone that has a professor that has a terrible accent, and it's impossible to understand anything he says. You are a life saver.
    I really appreciate your videos, thank you.

    • @daviemeister3355
      @daviemeister3355 4 ปีที่แล้ว +24

      Yeah, I severely hate when that happens! Its not that I dislike those teachers... they are really nice! The problem is that their accent does not just suit the job in which they are teaching! Are we all so for diversity that we forget that its not about how diverse the teachers are but how they get the point across to the students? I am doing quite well in advanced functions right now.. I had a teacher with terrible accent, so not only do I not naturally understand her, but I naturally tune out when its impossible to comprehend. I had to search and search on my own, just to keep up. I just hope you were able to do well in that class...

    • @mohamedwael566
      @mohamedwael566 4 ปีที่แล้ว +1

      Lol, same for me

    • @Em022
      @Em022 ปีที่แล้ว

      CC life in Seattle

  • @hannahdadoll5008
    @hannahdadoll5008 3 ปีที่แล้ว +87

    I was about to have a breakdown when I decided to open my TH-cam and search for tutorial, thank God I found this. This is a big help for someone like me who had a modular class. Thank u so much

    • @sparrow9735
      @sparrow9735 3 ปีที่แล้ว +2

      Same. I was just about to give up. Thank god I found this😭

    • @notsofiasco
      @notsofiasco 3 ปีที่แล้ว +4

      I'm still having a breakdown because I still can't understand because I am THAT dumb😭 I badly need a personal tutor😭

  • @arc1671
    @arc1671 4 ปีที่แล้ว +282

    should've done a problem that's first term was something other than a 1.

    • @jacebrowy1420
      @jacebrowy1420 3 ปีที่แล้ว +12

      Agreed but it still helps

  • @mpc7440
    @mpc7440 3 ปีที่แล้ว +1265

    There is a 100% chance that i will never use this for my nursing degree lol

    • @googlewebsite5953
      @googlewebsite5953 3 ปีที่แล้ว +67

      prbly not but ive heard theres a surprising amount of math involved in nursing

    • @twomarinesandadunce1107
      @twomarinesandadunce1107 2 ปีที่แล้ว +34

      Hey, a fellow nursing major using this bs

    • @bopiiq8947
      @bopiiq8947 2 ปีที่แล้ว +3

      honestly same

    • @jaybirdeclipse3971
      @jaybirdeclipse3971 2 ปีที่แล้ว +5

      Fr- as a future Vet/poultry science student(working on community College classes to go less into major debt lol)
      I'm never going to use this crap

    • @emberphoenix3039
      @emberphoenix3039 2 ปีที่แล้ว +8

      Lol I want to go into an artistic career and I feel the same way. 🤣

  • @tmerkury2813
    @tmerkury2813 6 ปีที่แล้ว +216

    World's best tutor

    • @Angeloyoutube835
      @Angeloyoutube835 4 ปีที่แล้ว +4

      Right. I’d rather have this guy as a teacher instead of my current one.

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      @velsiz6217 3 ปีที่แล้ว

      Seriously

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      @jeibi6483 3 ปีที่แล้ว +1

      Ikr, i feel like i owe this guy my life😳

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      @luisdiamante5541 3 ปีที่แล้ว +2

      Hes already got a high amount of subscribers just in 6 months! Before he was 500k+ subs. Now hes already 2M!!

    • @ireallylikehuskies9472
      @ireallylikehuskies9472 3 ปีที่แล้ว

      amen

  • @ghw024
    @ghw024 6 ปีที่แล้ว +302

    Hey I've been watching some of your calc videos and just wanted to say thanks for all the help, you are legit saving me from failing tomorrow, thanks!

    • @BrothersorTerraria
      @BrothersorTerraria 6 ปีที่แล้ว +1

      Goodluck man!

    • @sogeqt9188
      @sogeqt9188 5 ปีที่แล้ว +4

      just wanted to say that this is an Algebra 2 concept

    • @chekzz5352
      @chekzz5352 4 ปีที่แล้ว +8

      @@sogeqt9188 its present in cal, precalc, and sometimes in algebra 2

    • @Manny24_8
      @Manny24_8 3 ปีที่แล้ว +2

      @@sogeqt9188 I didn’t have it in my algebra 2 course lmao

    • @randommonkey4900
      @randommonkey4900 ปีที่แล้ว +1

      @@sogeqt9188 i never learnt it in alg2 just learning rn in precal

  • @tylerdruskoff9689
    @tylerdruskoff9689 3 ปีที่แล้ว +35

    It’s 1am and a school night. This hw is due tomorrow. Thank you so much

  • @chair1694
    @chair1694 ปีที่แล้ว +38

    This is a pretty consistent way of factoring high degree polynomials, there's no weird algebra manipulations, and it's very repeatable

  • @Gegajim
    @Gegajim 3 ปีที่แล้ว +23

    This voice introduces peace to my brain

  • @ToBreatheMusic
    @ToBreatheMusic 2 ปีที่แล้ว +7

    I am pursuing a psych degree through an online university and currently taking a math course. I have been stuck on this topic for about an hour now and began to feel very defeated. I watched your video, and a light bulb went off in my head. A million times thank you!

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    @oneandonlyjet3622 4 ปีที่แล้ว +30

    I would be like most others and say I'm watching your videos because my teacher sucks, but I for whatever reason fall asleep in my calculus class. Thank you for making your videos informative while remaining to the point. Doubt you'll read this, but thank you. Have a great day! :)

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      @abeehamakhi5148 4 ปีที่แล้ว +2

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    @user-rv4ep1bs2p 9 หลายเดือนก่อน +7

    i PRAY for you all my brothers and sisters who struggle may the LORD bless you with knowledge and understanding ASK and you shall recieve in LORD JESUS NAME AMEN!!!

    • @Austinator430
      @Austinator430 14 วันที่ผ่านมา

      That verse is taken way out of context. Matthew 7:7-8 “Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you."
      The context here is clearly that of salvation, NOT that of wordly riches, or assessment understanding, although God may provide such knowledge if He so chooses to.

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    @averyleahy6268 หลายเดือนก่อน +1

    I love you sir...I was on the brink of tears before finding this. Bless you.

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    @nitamac1312 6 ปีที่แล้ว +98

    YOU ARE A MATH ANGEL!!!!

  • @blackenwhite6190
    @blackenwhite6190 10 หลายเดือนก่อน +3

    I've been watching for 2 years now and just wanna say thank you so much this is really helpful

  • @1nonlytorres757
    @1nonlytorres757 3 ปีที่แล้ว +48

    "make sure this is a zero, if not, something is wrong" that scared me bruv. lol

  • @c0da625
    @c0da625 3 ปีที่แล้ว +14

    You’re a good teacher!!! Your videos are helping me with my maths. Thanks a lot man!!

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    @azuce2860 4 หลายเดือนก่อน +1

    this is the best channel existing in the entire youtube, thank you so much

  • @bltoliver13
    @bltoliver13 4 ปีที่แล้ว +9

    Definitely buying some merch after my final, you've saved me throughout my entire pre-calc class

  • @andreat.4071
    @andreat.4071 5 ปีที่แล้ว +3

    Grade 10 students here na hindi naintindihan ang turo ni ser Kaya nanood ng video nato ngayon!!!

  • @kingmac0058
    @kingmac0058 ปีที่แล้ว +1

    U teach better then my teachers u talk at a pace I can understand u

  • @willw4096
    @willw4096 ปีที่แล้ว +4

    1:50 "The purpose of the Rational Zero Theorem is for us to get the first zero, and then use that to get the others using synthetic divison."

  • @emperorshaggy7190
    @emperorshaggy7190 ปีที่แล้ว +1

    You really just explained everything math teacher has been trying to teach the class for the past 3 months in less than a half hour

  • @LifeWithJB1
    @LifeWithJB1 2 ปีที่แล้ว +1

    God bless this man fr…some of our math teachers don’t teach and just give the work but now I am understanding it!!!

  • @sebe1015
    @sebe1015 4 ปีที่แล้ว +26

    That second example was exactly one of my exam questions. Following your steps, I ended up getting them right before I watched how you solved for them. Thank you!

  • @allawayn1005
    @allawayn1005 4 ปีที่แล้ว +7

    Idk how I appreciate this. you’re phenomenal

  • @stickshiftstarship
    @stickshiftstarship 2 ปีที่แล้ว +1

    My instructor had us list all factors and try synthetic division over and over, your way is so much simpler! Thank you!

    • @lolerishype
      @lolerishype ปีที่แล้ว +1

      I suppose that method is technically more straightforward; but Organchem’s method is indeed faster.

  • @ill_sailtheoceaninsunset
    @ill_sailtheoceaninsunset ปีที่แล้ว +1

    Hi I just want to say your video toturials are amazing I easily get it

  • @georgesadler7830
    @georgesadler7830 2 ปีที่แล้ว +2

    MR. Organic Chemistry Tutor, thank you for an extraordinary introduction to the rational zero theorem. This powerful theorem explains how to find all the zeroes of a polynomial function.

  • @caribbeankpoplover
    @caribbeankpoplover 2 ปีที่แล้ว +3

    I watched this man’s videos when I was studying Engineering Math in university and now I’m watching him again to teach my students 😊

  • @jylztimothyacoba8463
    @jylztimothyacoba8463 3 ปีที่แล้ว +1

    So happy to have this type of teacher, i always understand his lessons this 2020......

  • @kokolin5876
    @kokolin5876 4 ปีที่แล้ว +25

    Thx for the saving my ass entire high school year

  • @yzabeltrevino
    @yzabeltrevino 2 ปีที่แล้ว +9

    Im just trying to be an art teacher

  • @CheatCodeSam
    @CheatCodeSam 5 ปีที่แล้ว +2

    always look for your videos when I have a problem in math. you got the best math videos on the net

  • @elainel7503
    @elainel7503 5 ปีที่แล้ว +3

    thanks so much, you did it much faster and easier than other tutorials

  • @purplejam1470
    @purplejam1470 ปีที่แล้ว +2

    Question about the first example, how did the -5x turns into ±3? (In the introducing example thingy)

  • @mindmate0
    @mindmate0 5 ปีที่แล้ว +876

    why do you always sound like you are kidnapped and forced to make tutorials
    great video nevertheless

    • @natckwan
      @natckwan 5 ปีที่แล้ว +48

      so we can get high marks on our test

    • @manalibisht6865
      @manalibisht6865 5 ปีที่แล้ว +75

      do u want him to act like a clown or something

    • @sora_is_my_dad420
      @sora_is_my_dad420 4 ปีที่แล้ว +27

      It factors the polynomials or else it gets the the hose again.

    • @ravenreyvillacastin6264
      @ravenreyvillacastin6264 4 ปีที่แล้ว +36

      He makes it because he cares , and why the hell would you care about his voice when you can learn more from him bro? He saves all the students in my school because our teachers are lazy , so we thank him on how he takes effort making these videos we dont have blank answers on our exams👎👎👎

    • @MrStrutxD
      @MrStrutxD 4 ปีที่แล้ว +5

      unfunny, stop trying to be.

  • @faysalarab
    @faysalarab 5 ปีที่แล้ว +14

    thank you professor *THE ORGANIC CHEMISTERY TUTOR* . YOU HELPED ME A LOT TBH

  • @excuhvis6221
    @excuhvis6221 4 ปีที่แล้ว +1

    This guy is a king!! Way better than those stupid ass videos my instructor provides

  • @Starwarp02
    @Starwarp02 4 ปีที่แล้ว +2

    Thank you, your video helped me learn a section the professor skipped over but was still needed for the final

  • @ANJ2688
    @ANJ2688 9 วันที่ผ่านมา

    Bro i understood it like piece of cake. I sat up all night and i was wracking my head on how to begin doing this thing and it just didn't click. Thank you so so so much.

  • @cerulean22b69
    @cerulean22b69 3 ปีที่แล้ว +1

    Ok this is way simpler than the ALEKS explanation, also I find your voice kinda calming, I like the calm way you explain everything it really helps cause I'm cramming again and super stressed right now.

  • @jayjoetenry7656
    @jayjoetenry7656 5 ปีที่แล้ว +9

    Thanks for the help man im in algebra II and this is really helping me

  • @alhassanmichael306
    @alhassanmichael306 2 ปีที่แล้ว

    In fact, you are helping a lot of people. May God bless you.

  • @blacktutor16
    @blacktutor16 ปีที่แล้ว +21

    please what if the coefficient of x^3 is not 1? will u multiply it by the coefficient or find their factors separately?

    • @person-cf3di
      @person-cf3di ปีที่แล้ว

      th-cam.com/video/W9OBqw2JLpE/w-d-xo.html this video explains it

    • @brysongummerus6481
      @brysongummerus6481 ปีที่แล้ว

      Find factors seperately

  • @user-ls2vf1sh5z
    @user-ls2vf1sh5z 6 หลายเดือนก่อน

    Had to pause at the second part, but did get the answer right. It's easy and manageable if you just take enough time to find the factors and stuff, very helpful.

  • @faithfowler7484
    @faithfowler7484 2 ปีที่แล้ว +2

    So what would you do if the leading coefficient isn't 1?

  • @Fusion4Dayz
    @Fusion4Dayz 4 ปีที่แล้ว +6

    I use your videos for linear algebra (eigen values / eigen vectors). Thank you so much!

  • @seff2451
    @seff2451 8 หลายเดือนก่อน

    im taking my final exam today and I can proudly say you pulled me through this course every single week without fail

  • @sarahdemonia5591
    @sarahdemonia5591 2 ปีที่แล้ว

    Thank you! I have a calculus pretest in a few days and this concept panicked me--but this video allowed the idea to come back to me and I am not as afraid anymore. Thank you!

  • @aruukane819
    @aruukane819 ปีที่แล้ว

    As a dude whos knowledge at math is Mid-Average,You have no Idea how much I want to thank you from the bottom of my heart for this lesson

  • @ME-sz6fw
    @ME-sz6fw 3 ปีที่แล้ว +1

    Thank you for teaching me what my teacher could not

  • @fin07
    @fin07 7 หลายเดือนก่อน

    this is helping me out immensely, thank youuuuu 😭😭

  • @WhoTFMadeThisChange
    @WhoTFMadeThisChange 2 ปีที่แล้ว

    I love you so much man, I can’t focus in class for some reason so you’re a saint to me

  • @jeffreybrasier794
    @jeffreybrasier794 2 ปีที่แล้ว

    I can't tell you how much I love your videos. You have countlessly saved my life from failing

  • @blatshesz.s7964
    @blatshesz.s7964 ปีที่แล้ว

    I tried to read this from my textbook and that was an awful experience. Watching this video helped to save my time

  • @evyeamdal
    @evyeamdal 2 ปีที่แล้ว

    I swear you are my favorite person alive

  • @jacebrowy1420
    @jacebrowy1420 3 ปีที่แล้ว

    I have a test today and I knew nothing so I watched a ton of ur vids on what I was learning and it helped a lot so thank u and pray I do good on my test

  • @reic.2748
    @reic.2748 ปีที่แล้ว +3

    How did you get the 3 in the first equation

  • @limitzlol7274
    @limitzlol7274 ปีที่แล้ว

    i just learned like a whole chapter of math that i had no idea what was happening in, in legit 2 minutes like one example and i get it
    thank u sm

  • @Thorite_Gem
    @Thorite_Gem 11 หลายเดือนก่อน

    This video is far more helpful than my professor was. Thank you so much!

  • @Abraham-gf1oi
    @Abraham-gf1oi 4 ปีที่แล้ว +16

    Oh my goshh. I still don’t understand and I don’t know what I’m doing wrong. You said if it doesn’t equal zero there’s a problem. What’s the problem!? I don’t know what I did!!!

    • @cassandrafitydjx7462
      @cassandrafitydjx7462 4 ปีที่แล้ว +6

      Remember factor theorem? If the polynomial is factor to the division, it should result into 0, if there is a remainder, then it is not a factor.

  • @user-nu7zi3oi3w
    @user-nu7zi3oi3w 6 หลายเดือนก่อน

    I just appreciate you for your best teaching it

  • @brendanyazzie2774
    @brendanyazzie2774 2 ปีที่แล้ว

    u explain it much easier than the book does, online school has its negatives

  • @anastasnikolov9396
    @anastasnikolov9396 4 ปีที่แล้ว +4

    Nice explanation, you could use Horner's method right from the start instead of plugging in the values manually. It would save you ton of computation and you would end up with new coefficients right when you find the root so it saves you some time. Still very nice video :)

  • @miss.tofunmi
    @miss.tofunmi ปีที่แล้ว +2

    My tests has been saved

  • @SomeRandom_personInTheInternet
    @SomeRandom_personInTheInternet ปีที่แล้ว

    THANK YOU SO MUCH FOR MAKING MY LIFE WAY EASIER!!!!!

  • @egg-jj4qr
    @egg-jj4qr 2 ปีที่แล้ว

    bro idk why but i feel calm when i hear this guy's voice in every video

  • @dylanbeckfest4046
    @dylanbeckfest4046 ปีที่แล้ว +2

    My algebra teacher literally did a couple problems in front of us and didn't explain anything and just expected us to figure it out. What. A. Clown. 🤡

  • @WTHnada
    @WTHnada 3 ปีที่แล้ว +5

    this is the first video ive seen him make a mstake in lol. its okay i trust you!

  • @idwpercy
    @idwpercy 5 ปีที่แล้ว +2

    just wanted to say thanks, you are explaining tons of math in a way that will allow even my dumb ass to pass my exam tomorrow

  • @Melisa-oz6kb
    @Melisa-oz6kb 6 ปีที่แล้ว

    YOU'RE SERIOUSLY THE BEST TUTOR EVER

  • @jayannej.rosete835
    @jayannej.rosete835 2 ปีที่แล้ว +2

    How is this useful in culinary again?
    "Oh can you please pass the remainder of the equation (5x²-17x-15)÷(x-4) amount of Oil please":)
    PS:(Thnx for the help though)

  • @ruyi7284
    @ruyi7284 2 ปีที่แล้ว

    you are better than my professor in the Uni

  • @victorw.2668
    @victorw.2668 2 ปีที่แล้ว

    I love you sir, I really do, making my questions no more questions.

  • @bnifacemwale1730
    @bnifacemwale1730 3 ปีที่แล้ว

    He has helped alot in my academic career

  • @mryeminaung
    @mryeminaung 4 ปีที่แล้ว +1

    Thanks you for your help.

  • @ahmadfarisnurmohdmazlan5532
    @ahmadfarisnurmohdmazlan5532 3 ปีที่แล้ว

    Thanks for the guide man, really need it. Wish me luck. Have an exam 2 hours from now.

  • @susheetofu
    @susheetofu 2 ปีที่แล้ว

    oh wow you teaching are so good tysm without you i would fail my test TYSM!!!!

  • @shyryTsr2k
    @shyryTsr2k 5 หลายเดือนก่อน

    Really wished to have seen a lead coefficient that wasn't (1) but oh well... and thank goodness this is a video that I can actually pause and catch up on because it felt really rushed in my opinion... Still it helps me up a lot so thank you. Just thought I'd let you know!

  • @rosiewoodland23
    @rosiewoodland23 ปีที่แล้ว +1

    Thank you so much, I've been struggling with this concept and you helped me tremendosly!

  • @lexus7154
    @lexus7154 5 ปีที่แล้ว +33

    what if the leading coefficient is > 1?

    • @Adrian-yk3et
      @Adrian-yk3et 5 ปีที่แล้ว +1

      for real

    • @johnmeinert6600
      @johnmeinert6600 5 ปีที่แล้ว +55

      p/q applies to all factors of p and q, so for example if the factors of p are 1, 2, 3, and 6, and the factors of q are 1, 2, and 4, then the possible roots are all the combinations of +/- p/q, so in this case: +/- ( 1/1, 1/2, 1/4, 2/1, 2/2, 2/4, 3/1, 3/2, 3/4, 6/1, 6/2, 6/4 ), and then when you take out fractions that equal the same thing it's just +/- ( 1, 1/2, 1/4, 2, 3, 3/2, 3/4, and 6 ). hope this helps!

    • @adaugoorji1585
      @adaugoorji1585 3 ปีที่แล้ว +7

      That’s the only reason I’m here but he didn’t teach that 😭😭😭

  • @maviskkakeza3987
    @maviskkakeza3987 ปีที่แล้ว

    Loving your teaching 👊

  • @jules7174
    @jules7174 4 ปีที่แล้ว

    You need an award, thank god he made smart people like you

  • @djdesad
    @djdesad 4 ปีที่แล้ว

    Thank you for the handy videos, allow me to get better preparation in college algebra.

  • @moof1232
    @moof1232 ปีที่แล้ว

    you are my savior man thanks

  • @yahyaadem5391
    @yahyaadem5391 3 ปีที่แล้ว +1

    Yes the videos from 2006 still helps

  • @saltystuka4119
    @saltystuka4119 3 ปีที่แล้ว +1

    You are an angel sir, thank you

  • @jeanettegomez9984
    @jeanettegomez9984 4 ปีที่แล้ว +2

    Learn a lot from your videos! Can you please make one with function table of fog gof fof etc.? Thanks!

  • @IsabelRodriguez-nv2ue
    @IsabelRodriguez-nv2ue 3 ปีที่แล้ว

    Thank you so very much. All your video lessons are great!. Thanks again!

  • @starlightakabane4686
    @starlightakabane4686 2 ปีที่แล้ว

    I LOVE YOU THANK YOU SO MUCH YOU SAVED MY LIFE

  • @alicebloomfield4295
    @alicebloomfield4295 3 ปีที่แล้ว

    This made my life so much easier!!!! Thank you so much 💗

  • @abenezerab7835
    @abenezerab7835 3 ปีที่แล้ว

    Wow u are the best. Man I don't know how can I thank you I am one of the best in maths, phy, Chemistry in the class b\c of u

  • @midwestmatcha
    @midwestmatcha 4 ปีที่แล้ว

    Still searching TH-cam for math help?
    Yes, and it works!

  • @seynawynn4974
    @seynawynn4974 2 ปีที่แล้ว

    By far my favorite TH-camr!!!! Thank you !!!