The Factor Theorem and The Remainder Theorem

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  • Опубліковано 1 січ 2025

КОМЕНТАРІ • 207

  • @budget7236
    @budget7236 4 роки тому +149

    11 years later this video is saving my butt for online classes

  • @concode102
    @concode102 9 років тому +128

    you sorta sound like prince zukko from avatar. It was bugging me this whole time and finally figured it out.

  • @timhorton2486
    @timhorton2486 9 років тому +7

    Thank you Mr. Anderson. I can't tell you how frustrated I was getting when I was doing my homework using my professor's horrible explanation (which wasn't one at all). You saved my night.

  • @jarrodcollins22
    @jarrodcollins22 3 роки тому +9

    I wish I found your channel years ago. Thank you for what you do. You are amazing🙏❤️

  • @mannacharya4088
    @mannacharya4088 7 років тому +15

    3:00 What kind of long division is that?I am from India and I have definitely not done something like this and if I do my maths teacher will give me zero.
    Edit: I was a lot younger when I wrote this comment. But now after getting into high level Calculus and stuff, I have understood the easiness of this method.
    But due to the procedure being beaten in my head, I still find doing full long division quicker because I am at the point I can do it mindlessly.

    • @sajiantony2920
      @sajiantony2920 7 років тому +1

      Aurora Production's I am also Indian and I can relate to you so much.

    • @mannacharya4088
      @mannacharya4088 7 років тому +3

      Saji Antony - True my friend, it is actually called synthetic division but it will never help in gaining marks in CBSE exams.

    • @zoe-bm9sc
      @zoe-bm9sc 7 років тому +1

      Aurora Production's
      It's synthetic division.

    • @nishusaini2154
      @nishusaini2154 4 роки тому

      My teacher will give slaps + (-3 marks)😜😜

    • @donuts4680
      @donuts4680 4 роки тому

      Remya TG it’s not only Indians. You learn this type of division in the more complex math I think to make it easier

  • @CrazyAboutBallet
    @CrazyAboutBallet 13 років тому +4

    This was great! I have an exam in two days and now I know what I'm doing thank you!!

  • @azy676
    @azy676 8 років тому +55

    Maybe drink a little water before you record such a long video next time! Hey, don't strain yourself, alright? Please take care of yourself ^_^ Thank you for the video! I understood it very well

  • @jeromel4563
    @jeromel4563 4 роки тому +2

    man good job you do alot better than the khan academy dudes it takes me forever to understand them

    • @RandyAnderson
      @RandyAnderson  4 роки тому +1

      Glad you found the video helpful. Study well.

    • @jeromel4563
      @jeromel4563 4 роки тому +1

      @@RandyAnderson hope you are staying well in this time of the virus

    • @RandyAnderson
      @RandyAnderson  4 роки тому

      @@jeromel4563 I'm doing alright, all things considered. Hope you are, too. Stay safe.

  • @itstulyp
    @itstulyp 11 років тому +26

    Everybody see that?

  • @lukebowlby530
    @lukebowlby530 3 роки тому +1

    My teacher is a good one, but he goes so quickly. This really helped me understand the factor theorem, and what it actually means. I saw the process of doing x-1)(2x^2-x... thank you for making this, you're a good teacher

    • @RandyAnderson
      @RandyAnderson  3 роки тому +1

      Thank you. I'm glad to hear you found the video helpful. Study well.

  • @TheTravisAustin
    @TheTravisAustin 10 років тому +120

    Helpful, but the spit sound in his mouth is driving me crazy XD Just swallow it man.

  • @Urbadkiddo
    @Urbadkiddo 3 роки тому +3

    thank you so much, I'm taking algebra 2 as a freshman in hs and this just saved my butt.

    • @RandyAnderson
      @RandyAnderson  3 роки тому

      You're welcome. I'm glad you found the video helpful. Study well.

  • @davitsprings4368
    @davitsprings4368 11 років тому

    Explained it WAY better than my math teacher did, she gives terrible notes. She moves fast and doesn't explain much. Thank you so very much, you should continue making awesome videos like this one!

  • @_-diparoo-_
    @_-diparoo-_ 11 років тому +1

    Thanks for spending the time on making this video, REALLY HELPFUL

  • @joshfarrell8888
    @joshfarrell8888 3 роки тому +2

    Thank you so much my teacher cannot teach this right and this was so helpful to understanding 🙏

    • @RandyAnderson
      @RandyAnderson  3 роки тому +2

      You're welcome. I'm glad you found the video helpful. Study well.

  • @muhsinchill
    @muhsinchill 5 років тому +10

    10 years later.... Still helpful for a kid in maths class who don't understand anything

  • @kamogelomotshweni4309
    @kamogelomotshweni4309 8 років тому +2

    Randy, please explain to me how to aproach a polynomial when the first 3 terms have powers of 4,3 and 2 respectively, instead of beginning with the cubed term.

    • @rahmamonsef5851
      @rahmamonsef5851 4 роки тому +2

      its been 3 years but i hope you solved it

  • @RandyAnderson
    @RandyAnderson  12 років тому

    If we are dividing by x-1, then the "k" is 1. Thus, the remainder is the same as the value f(1). In the case of this example, f(1)=0, which was the remainder you got after you divided. Make sense?

  • @phoenixwings6441
    @phoenixwings6441 11 років тому

    thank you for explaining it , I read it in text book and kind of got it, but not really. Now after you explained it I can see how they are related.

  • @kimberlygilmore5686
    @kimberlygilmore5686 10 років тому +1

    Now it makes sense!!! Great teaching skills

  • @jorge10928
    @jorge10928 14 років тому +1

    awesome video. i was able to understand this right away

  • @gamingnerd3218
    @gamingnerd3218 2 роки тому +1

    Great video sir really helped me...🎈❤️

    • @RandyAnderson
      @RandyAnderson  2 роки тому

      I am glad you found the video helpful. Study well.

  • @DonMcC123
    @DonMcC123 14 років тому

    Great Video Man!!! Helped me for my exam!

  • @IvanAraiza-u4s
    @IvanAraiza-u4s Рік тому +1

    Thank you so much for making this topic understandable!!!

  • @lajamaicana712
    @lajamaicana712 10 років тому +2

    you are a life saver. THANK YOU

  • @kevinhuynh4533
    @kevinhuynh4533 8 років тому

    What happens if one of the coefficients of the polynomial is unknown but they give us the factor of that polynomial? How do we find the unknown coefficient?

  • @TheZackBriggs
    @TheZackBriggs 14 років тому

    Where did your inspiration come from to share your math knowledge with the internet audience? Nice tutorial btw although I don't understand fully the part where you factored . I'll have watch a how to factor video to refresh my memory.

  • @FourBeatShufflin
    @FourBeatShufflin 5 років тому

    How does this affect when checking if (x-3i) is a factor?

  • @anapupavac1942
    @anapupavac1942 2 місяці тому

    video helped me understand very clearly thank you

  • @sparq8957
    @sparq8957 7 років тому

    why is the value not -1 at 2:03

  • @gabrielegenota1480
    @gabrielegenota1480 7 років тому +12

    Hmm... Nothing like my daily dose of ASMR!

  • @TurnrTheBurnr
    @TurnrTheBurnr 8 років тому

    Very helpful video nice work!

  • @StarPlusLove
    @StarPlusLove 12 років тому

    Sorry but I am to this and i dont understand where you got the numbers from at 3:24, can you explain please?

  • @edreannecalaycay
    @edreannecalaycay 13 років тому +1

    Thank you! Now I know I can ace my test tomorrow! XD

  • @sophiel6670
    @sophiel6670 9 років тому +5

    Scott Disick is that you?

  • @ladyb90luvme
    @ladyb90luvme 14 років тому

    hey thankyou for the vid. im not good at maths could you please explain how you get the quadratic after proving x-1 is a factor. please please i cant fail my maths exam. x

  • @giaomila3956
    @giaomila3956 5 років тому +4

    Im crying i cant understand

  • @arvinramonolos9805
    @arvinramonolos9805 8 років тому +3

    Bhow f(x)=(x-1)(2x*-x-6) become f(x)=(x-1)(2x+3)(x-2)?i didn't get it ☹️

    • @agerrgerra1361
      @agerrgerra1361 8 років тому

      The quadratic (2x^2 - x - 6) was factored into (2x + 3)(x - 2) in the second line, if you're still wondering. He just used the normal thinking method for that, nothing special.

    • @shariq6121
      @shariq6121 4 роки тому

      @arvin Actually it's a bit long procedure which we do in rough portion, So in 2x^2-x-6 , we will multiply the last value which is (6) to the coefficient of first term which is (2) with x^2.. right?
      We get '12' , Now we find factors of this 12, So by doing it we get 2×2×3 as factors of 12!
      Now you need to have two numbers such that it forms the middle value which '-x' , surely you have to take the highest one number to be negative and the other to be positive, so that our subtraction work is done ✅ and when we get the result it should include (-) sign with it.
      So 2×2×3 can be written as 4×3.. ok?
      These two values are for the middle term which is (-x), so by writing -4x+3x we will get the same (-x) value!! ..so this is correct.. now we will add this in place of our middle term value, so our expression will be like that:
      = (x-1) ( 2x^2 - 4x + 3x - 6)
      Now, we will take common between first two terms and last two terms,So:
      = (x-1) { 2x (x-2) 3(x-2)}
      Now as you see (x-2) is repeating so we will write it once in a bracket while the other common will also be gathered in other bracket of their own..So,
      = (x-1) (2x+3) (x-2)
      (2x+3) is the common we get from both terms, and (x-2) was the repeating bracket that we gathered.
      This method is actually called Middle-term-break
      Hope you get it!🙂

  • @jmdar9338
    @jmdar9338 4 роки тому

    How to determine if it is factor by just saying 0??

  • @neonWHALE002
    @neonWHALE002 14 років тому

    thank you so much :D the schooling system in spain sucks bad but you've helped a lot

  • @pictureversion
    @pictureversion 11 років тому

    now how do we work backwards when one of the factors is unknown....

  • @ObeyYourMind
    @ObeyYourMind 9 років тому

    aye bruh, how'd you factor all that hooplah?

  • @Kongol1000VEVO
    @Kongol1000VEVO 11 років тому

    You have helped me so much!!! Thank you.

  • @TheZackBriggs
    @TheZackBriggs 14 років тому +1

    You sound like a young instructor . I needed to watch this video again for my Final . Favorited!

  • @hessam97
    @hessam97 11 років тому

    I don't get how you got the "2X(squared)-X-6" from?

    • @richvaughn2622
      @richvaughn2622 11 років тому +2

      The original equation had the first term to the third power, so the answer is minus one less power, so it's to the second power. the 2x^2 is from the 2, the -x^1, or -x is the -1, and therefore the -6x^0, or -6 is the -6.

    • @KenrickM
      @KenrickM 10 років тому

      he dropped all the powers by 1, since he divided by "x"

  • @ara_seerwan
    @ara_seerwan 5 років тому

    What if the power of x is 4, so how can we factor if we have one divisor.

  • @Sham2951
    @Sham2951 15 років тому

    Now i know how to find other factors. Thanks!

  • @sambrock9861
    @sambrock9861 10 років тому +1

    great video thanks, so those zero's are your x-intercepts?

  • @amritkaur506
    @amritkaur506 11 років тому

    thank you ever so much :) keep it up and help us all with a maths problems :p

  • @sandras4805
    @sandras4805 10 років тому

    Does this method work for a negative factor? like, if you have a factor of (x+1) where x is -1. I tried to do it, but it didn't seem to work. Help!

    • @darenbalam1610
      @darenbalam1610 9 років тому

      +Sandra S if u have a factor (x+1) couldn't u just do (x -(-1)) ??? in that way u still have the (x-k) but setting it up that way would give u the positive one...sorry..im a year late DX

  • @alanoudalkhyeli3893
    @alanoudalkhyeli3893 5 років тому

    can you solve this equation : (8xto the pwer 3 -18xti the power 2 +21x -20) devide (2x-3)

  • @o1onewbeginningso1o
    @o1onewbeginningso1o 10 років тому

    so those zero's are also your x-intercepts

  • @shamamalamameh8838
    @shamamalamameh8838 11 років тому

    I completely understand where your coming from , honestly I have the same problem with all my teachers , but honestly if you think about it , you always have to presume that people already know something otherwise everytime you tried to teach something new to an audience you have no idea what type of people it consists of then each video is going to take an hour ...

  • @LiveGoodPhilippines888
    @LiveGoodPhilippines888 6 років тому +1

    thank you so much for this sir :) helps alot

  • @cincitymenace
    @cincitymenace 14 років тому

    Hi, this was on my recommended videos, when will I see this in college? Which class i mean

    • @TMoney53
      @TMoney53 4 роки тому +1

      im sure it’s too late now but i guess no response in nine years is your answer

  • @jacobdraculan961
    @jacobdraculan961 8 років тому +4

    I love you dude

  • @martin13mnm
    @martin13mnm 14 років тому

    You are simply amazing!

  • @jayrilambong9438
    @jayrilambong9438 6 років тому

    Thank you so much you help me for my test

  • @StereoSoundAgent
    @StereoSoundAgent 8 років тому +1

    i know they're interchangable but it's so annoying that my book will use (x-c), someone else will use (x-c) and then another youtuber will use (x-k) ... rad

  • @MsChadni
    @MsChadni 13 років тому

    Thank You so much... Helped me a lot!

  • @Keiran19
    @Keiran19 5 років тому

    Thanks! Was looking for this for a long time, phew

  • @pistalo1
    @pistalo1 12 років тому

    awesome. went to lecture class. picked up one or two things. this video, i have it locked

  • @dacdreamachieverclassesbyl8754
    @dacdreamachieverclassesbyl8754 6 років тому

    Where did 2 -1 -6 come from plz tell me

    • @shanaskibolton1095
      @shanaskibolton1095 6 років тому

      He added the values above them in the synthetic division table.

  • @Sameebob
    @Sameebob 13 років тому +2

    you have a nice friendly voice

  • @seph1109
    @seph1109 3 роки тому +1

    im fucking sobbing at 4am. i need to pass this worksheet or else i wont be able to take the exam later.

  • @user-ew5vj1sl1u
    @user-ew5vj1sl1u 3 роки тому +2

    Loved it.

  • @whatifwhynotwhere
    @whatifwhynotwhere 9 років тому

    1/6 = (-6) ? Why? Isnt suppose to be 1/6=(+6)

  • @xZetaa
    @xZetaa Рік тому +1

    You are awesome!!

    • @RandyAnderson
      @RandyAnderson  Рік тому

      Thank you. I'm glad you found the video helpful. Study well.

  • @AnnaaLambb
    @AnnaaLambb 12 років тому +1

    THANKS. THAT HELPED

  • @irahngio
    @irahngio 4 роки тому +2

    Firelord zuko why are you doing math

  • @raymond3235
    @raymond3235 5 років тому +1

    Thank you!!!

  • @TimRuffles
    @TimRuffles 14 років тому +1

    Good job! Couldn't get that from my textbook :D

  • @timhean
    @timhean 8 років тому +1

    U saved my life, thank u so much

  • @EngyPommy4
    @EngyPommy4 11 років тому

    Thanks, this helped a lot

  • @dacdreamachieverclassesbyl8754
    @dacdreamachieverclassesbyl8754 6 років тому

    Please tell me 2 -1 -6 how happened this

    • @Sophia-Luna
      @Sophia-Luna 6 років тому

      he used synthetic division.

  • @crockercharlotte
    @crockercharlotte 14 років тому

    Your dribble is distracting but the video was helpful! Thanks!

  • @lp6636
    @lp6636 3 роки тому

    bruh, I can just add them up like that?

    • @RandyAnderson
      @RandyAnderson  3 роки тому

      When doing synthetic division, yes. See: ua-cam.com/video/HzhNQ8a9rls/v-deo.html

  • @memohvictor7735
    @memohvictor7735 3 роки тому +1

    I love it!

  • @athenstube
    @athenstube 11 років тому

    Great video. Thank you!

  • @w00kokjin38
    @w00kokjin38 7 років тому

    nice!! Luv it so much

  • @EllipticalExistence
    @EllipticalExistence 14 років тому

    should buy a voice muffler thingy to cut out unnecessary mouth sounds.

  • @MattAlanKing
    @MattAlanKing 12 років тому

    Thanks, really helpful.

  • @afzal098765
    @afzal098765 8 років тому

    You are the best

  • @JUNEDWEEB
    @JUNEDWEEB 12 років тому

    Awesome video! :))

  • @Bubblevicious
    @Bubblevicious 13 років тому

    @EllipticalExistence Your comment made me LOL.

  • @kutloshalako8508
    @kutloshalako8508 9 років тому +2

    life saver

  • @stepbil
    @stepbil 13 років тому

    Great vid . thanks

  • @napartak
    @napartak 14 років тому

    well explained!

  • @abiegailecasio7234
    @abiegailecasio7234 4 роки тому +1

    Thanks

  • @AlexeyYunoshev
    @AlexeyYunoshev 7 років тому

    Thank you, sir

  • @Katasushi
    @Katasushi 6 років тому

    You never actually did anything on the Remainder Theorem. You read the description of it, then ignored it the rest of your video... You described the Factor Theorem, demonstrated it with an example, and then went on to even double check it... But you forgot about the Remainder Theorem... NOT HELPFUL!

  • @spookyghost7515
    @spookyghost7515 6 років тому

    Prince Zuko?

  • @marcorubio2962
    @marcorubio2962 13 років тому

    THANK YOU SO MUCH!

  • @tuana5127
    @tuana5127 7 років тому

    thank you so much!!

  • @BeckettSmeckett
    @BeckettSmeckett 6 років тому

    Explained this way better than my maths teacher.

  • @boostedthunder
    @boostedthunder 14 років тому

    They should introduce a love button

  • @FurleysAscot
    @FurleysAscot 12 років тому

    F (x)=this video was helpful

  • @bloomhot
    @bloomhot 10 років тому

    my equation is x4-3x3 + x2+x+4

  • @michaelismichael1
    @michaelismichael1 13 років тому

    honestly they should take all the online teachers and put them in class rooms instead of having horrible teachers

  • @lazert8144
    @lazert8144 11 років тому

    Good vid