Polynomial remainder theorem | Polynomial and rational functions | Algebra II | Khan Academy

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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!
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Опубликовано:

24 ноя 2014

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Комментарии : 149

@marissa1373 4 года назад

I was on the verge of tears during class because I didn’t understand this, but after watching 4 mins of this video it makes so much sense!!

@littlenewbie7172 Год назад

Kalm down

@srisaipatnaik2776 Год назад

same bro

@viacheddar 8 лет назад

Bless your souls at khan academy

@harishnarayanan1058 8 лет назад

so true!!!!!!!!!!!!!!!!!!!!!!!!!!1

@AbdullahKhan-mg8fm 6 лет назад

its 1 guy

@SuperDecimator 9 лет назад

Dear Khan, I guess I'll write it like a letter since the first comment was like that. Keep up the good work, you are much easier to understand than textbook lingo, and the colors are such a nice touch compared to whiteboards and black/white. Thanks much, A fan

@rhythm3869 6 лет назад

Anthony Cancellieri Youre welcome, An aircon

@icoudntfindaname 3 года назад

i wanted to like but u have 69 likes

@nitronight411 3 года назад

@@icoudntfindaname lemme do that 70.likes

@silaeraslan766 3 года назад

Sir, You make math seem simple. You have helped me more then you can ever know. Thank you and bless your soul.

@nirupatra8496 2 года назад

Yruci it f

@nameless4630 8 лет назад

dear Khan, this video helped me a lot and I understand this now so thank you so much! btw I love your voiceee yours sincerely, a fan

@sankalpt5240 6 лет назад

It's midnight for me and still I'm watching it 😊

@freakerzzzx 8 лет назад

exam tomorrow! this is one of the lessons!

@larryolive4829 4 года назад

good luck :)

@okokokkkkk Месяц назад

same

@ambarkranti3350 5 лет назад

Love the tutorial...It makes math so easy to understand ! :)

@einhacker-typ6457 8 лет назад

This was exactly what I was looking for!!!!! THANK YOUUUU

@clevergirl4457 4 года назад

This man and his initiative has saved a many lowly students from annihilation... Thank you so much Sal Khan!

@meh1561 4 года назад

your not talking about salman khan are you?

@arpangupta69420 3 года назад

Thanks for the video! I had a few doubts relating to this…all were cleared.

@yxsh6920 3 года назад

While byjus makes things more and more complicated with their so-called "visualization", Khan academy actually helps me understand concepts.

@biosavat9475 3 года назад

Really ? I don't think so , byjus has really helped me for years especially for maths but I always watch Khan academy's videos for revision

@reyaanahmed3163 Год назад

True....

@eswh8383 5 лет назад

Thank you Khan Academy for always helping me. 😀

@timothygreen158 9 лет назад

Dear khan, I do synthetic division instead of this. I would greatly appreciate it if you could make a video about it because I am a little bit confused on this subject. Sincerely, A fan

@flitzmazers4052 7 лет назад

yea synthetic division would be waay easier lol

@ari2102 3 года назад

Agreed.

@chicagotypewriter2094 Год назад

However, synthetic division can only be done on “x+-#” terms, long division can be done on anything But synthetic is so handy when the criteria is right!

@susavanmondal4522 2 года назад

He is teaching like other teacher but He is doing a magic to me Because after seeing his video I understood all the stuff. But before I was just struggling with that. ❤

@priyanshjain981 6 лет назад

I watched many videos but i am satisfied by your one...

@ComputerCurry 3 года назад

Great explanation from Sal Khan!

@facetiousmarbles3539 7 лет назад

1:02 seconds in and I understood EVERYTHING (About this). And I was sick for a whole week of polynomials too.

@imanabu5862 4 года назад

Same thing here!

@lowlag Год назад

thanks im in my precalc class this was an awesome video helpd a lot

@KDUlearning 4 месяца назад

I get it easily from you Thank you ❤

@sirikilohit2077 Год назад

WOW! In the first minute itself I've understood the remainder theorem!!!

@anoushkawadyalkar7514 7 лет назад

is there any video for factor theorem n how can it be used for factorization?

@abigailsarah4879 7 лет назад

really helpful

@sundersourot4234 7 лет назад

thank you khan academy

@tylerd8609 6 лет назад

Thank you for existing

@omanakuttan6038 3 года назад

Thanks sir...i get full in remainder theorem

@uzairhussain4856 2 года назад

great lecture...sweet wise

@serenehari 3 года назад

You saved my life, sir🙏

@josephpark9802 7 лет назад

where were you khan academy....i was searching for this kind of thing and now I've found it.

@riyathirukonda9397 Месяц назад

I love you khan academy

@anonymous___4999 6 лет назад

Thank u !

@ShivHanuman 2 года назад

Thank you sir

@token0855 6 месяцев назад

youve saved me oh my god, i really cannot thank you enough

@LockheartAesthetic 6 лет назад

So for everyone asking, f(1) came from f (a). If f(x) divided by (x-a) equals the equation that you are trying to solve, (x-1) is (x-a). So if (x-a) is what we use to find "a" then you only take the value for "a" and not the negative sign. This is because.... if "a" is negative, the sign will be positive and if "a" is positive the sign stays the same (negative) make sense? Example: if you are dividing by (x+2) then "a" is -2 because when you plug it in to (x-a) it looks like this (x-(-2)) which equals x+2. And if "a" is equal to 2 then plugged in to (x-a) it looks like (x-(2)) so x+2. Let me know if you need more help ^-^

@zaddydynamite 6 лет назад

Thanks! Makes sense but do you have any app i can communicate with you cause i need help on this

@lakshya1544 6 лет назад

Hey I want some help,if it is like the way you are saying it is. Then how would we proof the theorem by taking (x+2) because If you have watched the proof video of the theorem, It is proved using (x-a).If you haven't watched you can watch. Please help.

@santoshsharma-or4zu 2 года назад

@Lockheart, can you please help me with the proof for the remainder theorem ? In the proof I don't understand why x is substituted with a.

@devinhead43 7 лет назад

You are a better teacher than my teacher

@crontsquared230 6 лет назад

What is the program you use? Also on what software?

@tahmeenaakhtar3825 7 лет назад

thanks sir

@Brainrot69hd4k 4 года назад

sir guy!!!!! hand off!!!!

@tantelou2996 6 лет назад

Does the sign of "a" matter? What if it was divided by (x+1), would you use negative one when doing the theorem?

@karimhegazy3866 6 лет назад

tante lou you can think of it as x-(-1)

@keshav2262 3 года назад

No, it is not like that you should take f(a) = -1 in this, because we take f(a) value, the root of polynomial x + a, i.e -a, or if it is x - a then, f(a) = a ✌️✌️ Hope you like it

@presman2760 4 года назад

I disagree polynomial long division is a terrible way to start my morning

@horrordevil1413 3 месяца назад

Long division in 3rd-4th grade?!😮 We were taught this (not even directly) in 7-8 grade. 😢😢 what a curriculum

@padmap5415 5 лет назад

Math is fun and deadly

@krishivkaran5337 3 года назад

Deadly? How so?

@roseb2105 4 года назад

is the idea that you getting rid of the variables by dividing their degrees until it ends up with x to the power of zero (which 1 so that way get rid of the x and if im getting rid of the x I say what value do i plug into the equation to make x zero and isolate R?

@panetrist 5 лет назад

how did he do the last part to verify it?

@su1136 4 года назад

I really like your voice sir

@pointman6778 9 лет назад

Does long division get you to the same place as synthetic division?

@lolzlolzzxd 8 лет назад

yes. but synthetic division can only be used for linear factors, not quadratic factors

@thenotsobelligerentone 8 лет назад

+Russell Tan You can use synthetic division for quadratic functions :)

@radhababu4710 6 лет назад

yes

@Natsumi170 7 лет назад

Khan Academy uses Macs. Smart guys.

@md.ayaanahmed5152 2 года назад

"A little bit of polynomial long division is never a bad way to start your morning."

@ninadrangon 6 лет назад

is this same as long division???

@jesserealG 9 лет назад

late afternoon but good morning

@swethasai6389 4 года назад

Please say the definition of remainder theorem

@fareehafazelkhan6976 8 лет назад

this means you can take a as 1 and replace directly in f(x) no need to carry out the long division,is it good?

@erik9817 7 лет назад

Yes to obtain the remainder.

@snehalchougule7834 6 лет назад

Really it's very helpful for me......thanks KHAN ACADEMY.........

@shivanksharma772 8 лет назад

factorise it (x2+px+1) is a factor of (ax3+bx+c). solve it and prove a2-c2=ab

@radhababu4710 6 лет назад

liked it

@beautifulhennessy 6 месяцев назад

His voice>>>>>

@reynardminas5171 2 года назад

How about the exponent??

@fareehafazelkhan6976 8 лет назад

the long division is only for checking,right?

@kelseybee123 7 лет назад

Faree Far It depends. You can do long division OR synthetic division. I do long division instead of synthetic division bc it's easier for me, but that's just my preference.

@kabouch 4 года назад

Since f(x)= (Factor 1.Factor 2)+ Remainder, and Factor 1= (x-a), (a) is a solution that ends up with Factor 1. Factor 2=o, and consequently, f(x) = Remainder

@Alvinrasher 3 года назад

Love u khan academy I m a memer

@snehalchougule7834 6 лет назад

Do you have a video on topic 'French Revolution'?

@ari2102 3 года назад

Viva la revolution

@madrem 6 лет назад

Sal, why are we plugging in 1 into f(a) and then using that to substitute it into x

@hisyamhasbi8257 4 года назад

In case other people are wondering... U can understand it better if you watch the khan video about polynomial division. Basically f(x) is equal to multiplication of its factors + its remainder. In other words, F(x) = (divider) (result) + remainder In case of this video, F(x) = (x-1) (result) + remainder X is a variable right... That equation is valid for all value of x. And the point of this theorem is that we can actually get remainder without knowing the exact value of result. In this case, F(x) = (x-1) (result) + remainder If we just assume x is 1... (we can assume it as anything tbh) then the equation becomes F(1) = (1-1) (result) + remainder F(1) = (0) (result) + remainder Since result times 0 is 0, the value of result doesnt matter right? F(1) = remainder Voila!

@hamxahaxer7828 3 года назад

@@hisyamhasbi8257 love you man!!!!

@CaribbeanCryptoTips 2 года назад

Polynomial long division....not how I would start my morning lol

@BalaCliffDezjnr 2 года назад

Is it a -1 or just 1 ????

@HariKrishnan-bf4el 3 года назад

adipoli :)

@madrem 6 лет назад

Sal you also forgot to mention that x=a. Good video tho

@olgamaria8975 3 года назад

Professors should link khan academy videos in their online classes instead of their monotonous colleagues that only solve the problem and don't explain anything

@ridaasim3753 3 года назад

mine actually did-

@yohannesmeseker1354 4 года назад

you are my best teacher but now day you are not uploading new videos

@shambhavi2191 5 лет назад

I was wondering isn't a=-1 ?

@harshmittal1570 8 лет назад

Y can't I give more than one like😎😎😎😎

@drharishdubey5471 4 года назад

i am watching this while online class

@pmcforever9686 4 года назад

can someone plz tell me what is causing the click sound @ 1:20

@ari2102 3 года назад

This is more intresting than the video itself. I know for a fact that its not a pen because he is on a computer, it cant be hhis mouse as we cant hear it throughout the video so he must be using a drawing board pen that artist on paper use to make digital art which explains the handwriting so it must be the pen hitting the board a bit too hard but thats just a theory.

@deshiyer7573 8 лет назад

thankthankthankyouyouyouyouyouyousosososososososososososososmuchmuchmuchmuch!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

@JaffreyH 6 лет назад

where did f(1) come from?

@iaexo 6 лет назад

Jaffrey H the theorem says that the remainder should be f(a) when divided by x-a, and since in this case a=1, it would be f(1). Hope this helps!

@gauravGupta-bk2sw 11 месяцев назад

If f(x) is divided by x-a,remainder= f(a)😊

@Chococat3646 7 лет назад

I AM THE SMARTEST PERSON NOW

@ImThunder7 3 года назад

what is the meaning of f(x) or something like f(""random letter"") and meaning of f random letter here can be (a,b,c,.......)

@simranchahal4811 3 года назад

f is a function , means f inputs x and outputs a .

@mrprogamer896 7 лет назад

Become my teacher.plz.

@prantoshnaha5114 6 лет назад

But how do you determine the value of a???

@donuts4680 4 года назад

It’s where the divisor is

@ari2102 3 года назад

You dont. The value of a is given

@rhythm3869 6 лет назад

what if its ÷ (3x-1)???

@RunningPeas 3 года назад

I dont know if you still need this but it never does

@Jchinterior 3 года назад

APEC LANG MALAKAS HAHAHHA

@flapcow6837 Год назад

its morning =

@idirtyhands8957 7 лет назад

"...we deserve a minor drum roll." hahahahha

@maheenrida 4 года назад

No one: Him: "divisOHr" 😂

@StewV 2 года назад

yo i know your son he goes to my friends school

@saintshaggy1372 6 лет назад

It's a little wrong The remainder is f(x) which is 1 when x-1=0, as a = -1 not 1

@LockheartAesthetic 6 лет назад

So he is solving for the remainder, not for the roots, this problem essentially asks if x-1 is a root and if it is able to be factored evenly. The answer here is no so we don't solve for the roots. Also, solving for a is different than solving for x because x-1 is not equal to f(x) here, it is being divided by f(x) instead.

@mohammedthaier1718 2 года назад

It feels like magic

@andresfigueroa3017 7 лет назад

It's asking me too find the remainder without using long division 😫😫

@sandlasenkosingcobo2374 15 дней назад

Sal is goated🫡

@papeeha3172 7 лет назад

Tomorrow's my maths exam...wish me luck!😊☺

@poolaramesh5066 4 года назад

What I can I do because is over

@rounaqqureshi7887 Год назад

I was see in 2023

@jessicafelisha8161 6 лет назад

Why does f(1)=R come from X-1 but f(-1)=R come from X+1 shouldn't it just both be 1 cos (X-a) you're just taking the a value? I don't understand .:/

@LockheartAesthetic 6 лет назад

Jessica Felisha yes you take the a value only. If you had (x+2) then "a" would equal -2 because it has to be the opposite of the rule to make the rule work. If the remainder is 2 then you are dividing by (x-2) not (x+2). Make sense? Kind of like equations for circles when they ask you to find (h,k)

@LockheartAesthetic 6 лет назад

If a is -1 then you plug it in as (x-(-1)) which equals (x+1) if a is 1 then you plug it in (x-(1)) so (x-1) make sense? Sorry if it's too complicated I really want you to understand

@scrapergaming609 3 года назад

Ggs

@scrapergaming609 3 года назад

Yyoyoy

@allkindzzz9847 6 лет назад

Khan died for our sins

@dustynbennett3826 7 лет назад

God loves you. I wanted you to know that. He sent his son to die on the cross for your sins. He rose again three days later so that through His life, death, burial and resurection we may have forgiveness of our sins and new life through Jesus Christ if we only ask him for forgiveness of our sins and believe in God and that Jesus is God's son, and also that God rose Him from the dead. and also confess Jesus Christ as your Lord and Savior for ever more!

@anoushkawadyalkar7514 7 лет назад

Dustyn Bennett why are you commenting this stuff on some educational video? go n search for some superstitious stuff and comment