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

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/alge...
Basic algorithm for Synthetic Division
Watch the next lesson: www.khanacademy.org/math/alge...
Missed the previous lesson?
www.khanacademy.org/math/alge...
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
/ channel
Subscribe to Khan Academy: kzread.info_...

Пікірлер: 237

  • @GavinWilliamsTheGreat
    @GavinWilliamsTheGreat7 жыл бұрын

    I love learning math at home because i can say "Oh shitttttt" and "HELL YEAHHH" whenever i get something.

  • @madisoncarman9628

    @madisoncarman9628

    6 жыл бұрын

    Gavin Williams SAME omg

  • @loisannebarin6995

    @loisannebarin6995

    5 жыл бұрын

    Same 😂😂

  • @moahammad1mohammad

    @moahammad1mohammad

    4 жыл бұрын

    Good job gavin

  • @graceli8992

    @graceli8992

    3 жыл бұрын

    Just to say, I don't swear

  • @Geeloveesu

    @Geeloveesu

    3 жыл бұрын

    Same 👌🏽🤣

  • @antisocialblender9505
    @antisocialblender95055 жыл бұрын

    I just love how I can learn in five minutes what takes a normal teacher 30 minutes to teach thanks

  • @MasterCivilEngineering

    @MasterCivilEngineering

    3 жыл бұрын

    Absolutely dear❤❤❤

  • @allyconnie9619
    @allyconnie961910 жыл бұрын

    He makes me laugh sometimes "it may seem like voooodoooo" :P

  • @sohankesineni870
    @sohankesineni8705 жыл бұрын

    My class is for 40 minutes. I do not understand a thing my teacher is saying but you taught it to me in 6 minutes. Thank you

  • @MasterCivilEngineering

    @MasterCivilEngineering

    3 жыл бұрын

    Great dear

  • @gamerprince-tl5hg
    @gamerprince-tl5hg8 жыл бұрын

    Wasn't paying attention in class today so I missed this lesson in class... Thanks!

  • @britneycampbell8696

    @britneycampbell8696

    6 жыл бұрын

    gamerprince1999 same honestly

  • @traceputtz

    @traceputtz

    5 жыл бұрын

    same lol

  • @monononny3974
    @monononny397410 жыл бұрын

    middle schoolers up in here sayin they're doin this, meanwhile I'm in college having to do this DX

  • @tinaandersen3270

    @tinaandersen3270

    6 жыл бұрын

    Don't feel bad. I am in the same boat.

  • @alexlucas6666

    @alexlucas6666

    3 жыл бұрын

    Same, mate

  • @animationspace8550

    @animationspace8550

    3 жыл бұрын

    And now you are 7 years past college and I hope your life is doing good

  • @monononny3974

    @monononny3974

    3 жыл бұрын

    @@animationspace8550 nope

  • @lordspotato5032

    @lordspotato5032

    3 жыл бұрын

    f

  • @MrCookN7
    @MrCookN78 жыл бұрын

    when exams are coming up and u need to be refreshed

  • @tinaandersen3270

    @tinaandersen3270

    6 жыл бұрын

    Or when you are behind in math.

  • @loisannebarin6995

    @loisannebarin6995

    5 жыл бұрын

    @@tinaandersen3270 me

  • @Shotgun93Alexander

    @Shotgun93Alexander

    5 жыл бұрын

    I have an exam on Wednesday

  • @christinetomer205

    @christinetomer205

    5 жыл бұрын

    Mood I have a midterm tmrw

  • @colec2062

    @colec2062

    4 жыл бұрын

    Timeless comment

  • @shobysstories5972
    @shobysstories59723 жыл бұрын

    I am currently struggling in math because of today's online classes due to this covid... this video helped me a lot and I want to thank Khan Academy for this... Love from the Philippines!

  • @GerrrFace
    @GerrrFace10 жыл бұрын

    Thanks! I'm in 9th and I'm in algebra 2 honors, and my teacher doesn't describe the lesson well this helps a lot! *subscribe* you make it easyer to understand! Precal and algebra 1 for collage here i come! (Nxt year) ;-; ~tear

  • @super_heroes

    @super_heroes

    6 жыл бұрын

    Taryn Mccain why do you have to re-take algebra 1?

  • @ryleesmith-taylor7433

    @ryleesmith-taylor7433

    6 жыл бұрын

    Nico Johnston he said it's collage tier algebra 1.

  • @super_heroes

    @super_heroes

    6 жыл бұрын

    wow I feel stupid, thanks though

  • @jeanciliacherizar7836

    @jeanciliacherizar7836

    5 жыл бұрын

    Omg same 7th grade here taking alegebra 1 gotta prepare for a test Yikessss😫😫😥😥

  • @yashuppot3214

    @yashuppot3214

    4 жыл бұрын

    I took calc in 8th grade, i feel your pain

  • @ManicStreetPigeon
    @ManicStreetPigeon7 жыл бұрын

    Extremely helpful, thanks a bunch

  • @Tamil350
    @Tamil350 Жыл бұрын

    This is extremely helpful for me. Even though im just grade 8, the teach me the topics of 9th or 10th. While my sir was teaching, I couldnt understand. But now I can see everything coming together. Very very thank you❤

  • @ClovisMint
    @ClovisMint6 жыл бұрын

    for the bottom equation, the one that your dividing by all your doing is finding the zero of it/roots so basically X+4 is X+4=0, that's why it is -4 and if you graph y=x+4 the root aka x-int is -4 same if you divide the polynomial by x^2-1, you find the zeros which are 1 and -1 and use it for the synthetic division(same place the -4 was put in the videos example)

  • @Ch1n4Sailor
    @Ch1n4Sailor7 жыл бұрын

    I've always heard, "Set (x + 4) = 0" But same concept, same result using the negative of 4 ( -4 )

  • @bril5842
    @bril58425 жыл бұрын

    Im an 8th grader and we are doing this in Pre Ap Algebra 1 i didnt get it when my teacher explained it so so but this helped a lot thanks

  • @gold4963
    @gold49636 жыл бұрын

    Ah, thanks so much! Kahn Academy is awesome!

  • @Animerulespeople
    @Animerulespeople4 жыл бұрын

    lol people need to stop bragging about what age they're learning this at

  • @MasterCivilEngineering

    @MasterCivilEngineering

    3 жыл бұрын

    Yeah dear

  • @maged2011g
    @maged2011g8 жыл бұрын

    thank you👌🏼

  • @vrushabh1010
    @vrushabh10103 жыл бұрын

    4:07 "drumroll right over here" isn't he the best :'))

  • @itzjay2002
    @itzjay20025 жыл бұрын

    thank you very much very helpful!

  • @fatffatable
    @fatffatable9 жыл бұрын

    Amazing video; thank you very much

  • @George_haddad1997
    @George_haddad199711 жыл бұрын

    Thanks for sharing...

  • @Xjshadow
    @Xjshadow5 жыл бұрын

    This has saved me from having the most miserable night of precalc in my life. Many thanks!

  • @biganakan5508
    @biganakan55086 жыл бұрын

    Thank you sooo much.It help alot

  • @ginikaezeokoli378
    @ginikaezeokoli3783 жыл бұрын

    Thank you so much. You explained it better than my teacher.

  • @queNWS
    @queNWS7 жыл бұрын

    10 questions 1. Are you sure you cant do it with coefficient? do you know binary?

  • @angieorais2864
    @angieorais28645 жыл бұрын

    yow! thanks so much it will soon help in my ft tomorrow because i got zero on my 2 ft hopefully it will develop my score

  • @lilcutiepie11234
    @lilcutiepie1123411 жыл бұрын

    this is so much easier than long division with polynomials

  • @shrinand13
    @shrinand137 жыл бұрын

    Thank you

  • @muhammadamin7487
    @muhammadamin7487 Жыл бұрын

    Ma Sha Allah. Nice. Thanks.

  • @droopyeyedmofo5618
    @droopyeyedmofo56186 жыл бұрын

    I prefer traditional long division but I had a problem that it didn't work for. Please tell me if i am making simple mistakes or synthetic only works for this problem. PROBLEM: (x⁴−3x³+x-4)(x+1)

  • @droopyeyedmofo5618

    @droopyeyedmofo5618

    6 жыл бұрын

    Ehh I kinda figured it out but I'll leave this comment, I was putting an unnecessary negative sign

  • @Yakushii
    @Yakushii12 жыл бұрын

    I also prefer normal long division, even for polynomials. But I haven't seen the synthetic division before. :)

  • @lilykate4270
    @lilykate42706 жыл бұрын

    You have saved my life!

  • @bjornironborn8967
    @bjornironborn89677 жыл бұрын

    Dude thanks! you helped.

  • @-thesignpainter9486
    @-thesignpainter94863 жыл бұрын

    idk what this guy's name is, but he's my favorite on khan academy

  • @jupitersky

    @jupitersky

    2 жыл бұрын

    Sal Khan, the founder of Khan academy. He's my favorite as well :D Love the World of Goo reference btw!

  • @fortyeu789
    @fortyeu7897 жыл бұрын

    Sal Khan is the math god in human form.

  • @MissJukeBox8
    @MissJukeBox85 жыл бұрын

    FINALLY I UNDERSTAND HOW THIS WORKS!

  • @sawensh8223
    @sawensh822312 жыл бұрын

    GOD job thanks

  • @xzelvimarauson3564
    @xzelvimarauson35646 жыл бұрын

    This video is very helpful especially for me because we are just in 8th grade but we are already studying about thism

  • @venkataraogandivalasa7845
    @venkataraogandivalasa78453 жыл бұрын

    Thanks!!! For a really effective explaination.. I think I finally understood something in math😂😂😂.

  • @earthchan3358
    @earthchan33582 жыл бұрын

    Great video!

  • @JDB51
    @JDB514 жыл бұрын

    but what part is the remainder and what part is the quotient? the remainder would be the last term on the bottom right? and then would the quotient just be the original x-a term?

  • @user-qc4sl1mk1b
    @user-qc4sl1mk1b7 ай бұрын

    So what if the bottom is already a negative, do you keep it as is or change the sign to positive?

  • @bimalashrestha3616
    @bimalashrestha36165 жыл бұрын

    Really nice....sir

  • @raphaelspalding
    @raphaelspalding12 жыл бұрын

    thanks sal

  • @huhwoah4115
    @huhwoah41156 жыл бұрын

    pure magic

  • @tinaandersen3270
    @tinaandersen32706 жыл бұрын

    I hope that this video is more helpful then the other video.

  • @AmazDMC
    @AmazDMC7 жыл бұрын

    Dude! what method are you using?

  • @lonewolf2612
    @lonewolf26124 жыл бұрын

    Thank u so much....i have an exam today..

  • @muhammadsaleembhatti516
    @muhammadsaleembhatti5162 жыл бұрын

    Sir please make a video or tell me the derivation of synthetic divsion

  • @snakedron
    @snakedron9 жыл бұрын

    you da man thanks

  • @becalmandquiet881
    @becalmandquiet8813 жыл бұрын

    Great video

  • @JohanJpPaul
    @JohanJpPaul11 жыл бұрын

    Nice.

  • @kaushikrao2932
    @kaushikrao29326 жыл бұрын

    i love ur language...cool

  • @shasessau
    @shasessau5 жыл бұрын

    WOOWW BUT THE NEGATIVE IS CONFUSING ME

  • @JEE2025ASPIRANThere
    @JEE2025ASPIRANThere27 күн бұрын

    Thanks

  • @SnackPack_Gaming
    @SnackPack_Gaming11 жыл бұрын

    does he have a video of the extra bells and whistles required to do this when the coefficient of your divisor isn't 1?

  • @paultejada7828
    @paultejada78283 жыл бұрын

    America: its so hard Philippine: u Sure about that

  • @arhamsaeed957
    @arhamsaeed9576 жыл бұрын

    At the start what if it's already negative do we change it into positive

  • @britneycampbell8696
    @britneycampbell86966 жыл бұрын

    Question.. why do you change the +4 on the bottom to a negative in dividing?

  • @ogzelle

    @ogzelle

    6 жыл бұрын

    Britney Campbell You set it equal to zero, x+4=0, subtract 4 from both sides, *boom* you get -4

  • @jeromethebuffgnome
    @jeromethebuffgnome12 жыл бұрын

    Yee thank you ShakaKHAN

  • @rosal2482
    @rosal24823 жыл бұрын

    Thanks I get it noa

  • @Necrofang214
    @Necrofang21412 жыл бұрын

    my dad made me learn this over summer break. and im in 7th grade. and ive forgotten already.

  • @divyoroy9056
    @divyoroy90565 жыл бұрын

    I have one question sal at 2:28 is there a reason why u have to take the negative?

  • @pikachurro2295
    @pikachurro22956 жыл бұрын

    IT IS VOOOOOODOOOOOO!!

  • @SweetFiyaa
    @SweetFiyaa10 жыл бұрын

    Cool

  • @rileysondermann6328
    @rileysondermann63284 жыл бұрын

    Why is khan academy more helpful than my math teacher

  • @godsyogurtgun

    @godsyogurtgun

    4 жыл бұрын

    Because in your classroom there are abunch of kids and because the teacher is helping everyone not one person at a time

  • @siragan4369
    @siragan43695 жыл бұрын

    HAVING THE BOARD BLACK AND THE WRITING SO MINUTE MAKES IT A BIT AWKWARD...DON'T YOU THINK SO!???

  • @jaggedsigns3O11
    @jaggedsigns3O117 жыл бұрын

    I find this video offensive I'm an active voodoo conjurer.

  • @Christian-bj4rp

    @Christian-bj4rp

    4 жыл бұрын

    your joking right

  • @jcl_piano

    @jcl_piano

    4 жыл бұрын

    Lol I don't think Ian is 😂😂

  • @godsyogurtgun
    @godsyogurtgun4 жыл бұрын

    Was being an idiot and didn't do my work during thie quarantine and now i gotta do it

  • @777bailey
    @777bailey Жыл бұрын

    you are a life saver thank you

  • @Otaku_chan-bi9wv

    @Otaku_chan-bi9wv

    Жыл бұрын

    Why

  • @777bailey

    @777bailey

    Жыл бұрын

    @@Otaku_chan-bi9wv because i just got an 100 on my test duhh

  • @JishiChan
    @JishiChan5 жыл бұрын

    I have an exam tomorrow and finals next week :’) IM DOOMED JVKCK K K

  • @amrutabhoi8950
    @amrutabhoi89507 жыл бұрын

    today is my exam lol thbx

  • @halena539

    @halena539

    7 жыл бұрын

    amruta bhoi How'd you do lol?

  • @amrutabhoi8950

    @amrutabhoi8950

    7 жыл бұрын

    Following The Most High I solved by the same synthetic method As shown in video

  • @jpb9876

    @jpb9876

    7 жыл бұрын

    amruta bhoi same, mines tomorrow 😂

  • @VeyronSolar

    @VeyronSolar

    7 жыл бұрын

    Mines tomorrow also XD

  • @moh5938

    @moh5938

    7 жыл бұрын

    Bro at least it's an exam , i got a SAT exam tomorrow and I didn't know this

  • @assasindan_1236
    @assasindan_12367 жыл бұрын

    do synthetic division with numerical coeficient do it if its no voodo magic!!! #dooksrR'us

  • @bricklord5017
    @bricklord50172 жыл бұрын

    Anyone else wonder how his handwriting is so good?

  • @pbz7572
    @pbz75725 жыл бұрын

    But why is the 4 negative?

  • @Slowcomputerguy
    @Slowcomputerguy10 жыл бұрын

    My mind just got fucking blown.

  • @jennacarvalho5369
    @jennacarvalho53694 жыл бұрын

    Who invented this, long division makes so much more sense in my opinion

  • @crontsquared230
    @crontsquared2306 жыл бұрын

    So the last term is always the remainder?

  • @user-rr2hu7yj3g
    @user-rr2hu7yj3g3 жыл бұрын

    I am 9 years old. Why is this in my recommendations.

  • @007MrYang
    @007MrYang12 жыл бұрын

    LOL I can't stop laughing, that's exactly what I thought.

  • @Jordinilini
    @Jordinilini11 жыл бұрын

    Holy shit, Mind Blown.

  • @zombiedude347
    @zombiedude3474 жыл бұрын

    All my math teachers got confused when I used synthetic division. I just felt the "traditional" way took up way too much space.

  • @MasterCivilEngineering

    @MasterCivilEngineering

    3 жыл бұрын

    ❤❤❤👍👍👍

  • @tinytitan1147
    @tinytitan11475 жыл бұрын

    What happens if the bottom is 2x +8?

  • @BobbieDraper
    @BobbieDraper3 жыл бұрын

    i hate online classes...

  • @beepbloop5958
    @beepbloop59588 жыл бұрын

    Hey, I don't understand you said there would be square 3 but where is the x coming from?, should I just follow that without any reason? please help.

  • @JamesTownsendJian

    @JamesTownsendJian

    8 жыл бұрын

    The 3 itself isn't getting squared. It's the X that's getting squared. After setting aside the remainder, you start with the constant (30) and take it from there by increasing the power by one as you move from the right to the left. So you have 30, then -8x (or -8x^1), then 3x^2. If he had ended up with more numbers, the powers would keep increasing by one. So for example, and this is only an example mind, assume he'd ended up with 8, 5, 3, -8, 30 and -121. In this case, he would set aside the -121 as the remainder and again start on 30. That would be 8x^4, 5x^3, 3x^2, -8x and 30. I hope this helped. :)

  • @giggles8593
    @giggles85933 жыл бұрын

    Sal to the rescue

  • @Miawgician
    @Miawgician5 жыл бұрын

    Who watched this video bcuz u have Quiz for Calculas tomorrow

  • @jemuellgaudia8512
    @jemuellgaudia85126 жыл бұрын

    I am so stress about our test tomorrow because i don't know how to do it.

  • @marcotrolo3134
    @marcotrolo31347 жыл бұрын

    VOODOO MAGIC

  • @masternbt
    @masternbt12 жыл бұрын

    I just learned this lol

  • @Menegoth
    @Menegoth12 жыл бұрын

    Isn't this a Horner scheme?

  • @swea2827
    @swea2827 Жыл бұрын

    top g

  • @godjihyo5708
    @godjihyo57084 жыл бұрын

    Feels a lil’ bit lonely to be an 8th grader amongst sophomores and graduates.. 👉👈

  • @intoxicatingGold
    @intoxicatingGold12 жыл бұрын

    i learned this with a different name, theorem of someone

  • @kasasuka9590
    @kasasuka95904 жыл бұрын

    i hope this saves me from failing

  • @McUseless1
    @McUseless112 жыл бұрын

    What sorcery is this?

  • @shivdesai1
    @shivdesai112 жыл бұрын

    First time I've ever been early to class.

  • @spaniard1914

    @spaniard1914

    6 жыл бұрын

    What are the daily applications for this type of math?

  • @SuperBonman
    @SuperBonman11 жыл бұрын

    Are you a wizard?

  • @E_E_Bro
    @E_E_Bro10 жыл бұрын

    thumbs up if your in seventh grade.

  • @shannenpaige2590
    @shannenpaige25905 жыл бұрын

    taking my exams later and still watching this tho! much needed!!!