Polynomial remainder theorem | Polynomial and rational functions | Algebra II | Khan Academy
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- Опубліковано 24 лис 2014
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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!!
Kalm down
same bro
Bless your souls at khan academy
so true!!!!!!!!!!!!!!!!!!!!!!!!!!1
its 1 guy
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
Anthony Cancellieri
Youre welcome,
An aircon
i wanted to like but u have 69 likes
@@icoudntfindaname lemme do that 70.likes
Sir,
You make math seem simple.
You have helped me more then you can ever know.
Thank you and bless your soul.
Yruci it f
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
exam tomorrow! this is one of the lessons!
good luck :)
same
This man and his initiative has saved a many lowly students from annihilation...
Thank you so much Sal Khan!
your not talking about salman khan are you?
It's midnight for me and still I'm watching it 😊
Love the tutorial...It makes math so easy to understand ! :)
While byjus makes things more and more complicated with their so-called "visualization", Khan academy actually helps me understand concepts.
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
True....
This was exactly what I was looking for!!!!! THANK YOUUUU
Thanks for the video! I had a few doubts relating to this…all were cleared.
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. ❤
Thank you Khan Academy for always helping me. 😀
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
yea synthetic division would be waay easier lol
Agreed.
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!
I watched many videos but i am satisfied by your one...
1:02 seconds in and I understood EVERYTHING (About this). And I was sick for a whole week of polynomials too.
Same thing here!
thanks im in my precalc class this was an awesome video helpd a lot
WOW! In the first minute itself I've understood the remainder theorem!!!
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 ^-^
Thanks! Makes sense but do you have any app i can communicate with you cause i need help on this
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.
@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.
Great explanation from Sal Khan!
I get it easily from you Thank you ❤
thank you khan academy
really helpful
Thank you for existing
Math is fun and deadly
Deadly? How so?
Thanks sir...i get full in remainder theorem
You saved my life, sir🙏
great lecture...sweet wise
I love you khan academy
youve saved me oh my god, i really cannot thank you enough
Thank u !
where were you khan academy....i was searching for this kind of thing and now I've found it.
Thank you sir
is there any video for factor theorem n how can it be used for factorization?
You are a better teacher than my teacher
thanks sir
Long division in 3rd-4th grade?!😮 We were taught this (not even directly) in 7-8 grade. 😢😢 what a curriculum
sir guy!!!!! hand off!!!!
Does the sign of "a" matter? What if it was divided by (x+1), would you use negative one when doing the theorem?
tante lou you can think of it as x-(-1)
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
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
mine actually did-
I disagree polynomial long division is a terrible way to start my morning
I really like your voice sir
What is the program you use? Also on what software?
Khan Academy uses Macs. Smart guys.
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?
"A little bit of polynomial long division is never a bad way to start your morning."
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?
Yes to obtain the remainder.
Really it's very helpful for me......thanks KHAN ACADEMY.........
factorise it (x2+px+1) is a factor of (ax3+bx+c). solve it and prove a2-c2=ab
late afternoon but good morning
Does long division get you to the same place as synthetic division?
yes. but synthetic division can only be used for linear factors, not quadratic factors
+Russell Tan You can use synthetic division for quadratic functions :)
yes
His voice>>>>>
liked it
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
Do you have a video on topic 'French Revolution'?
Viva la revolution
is this same as long division???
the long division is only for checking,right?
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.
adipoli :)
Love u khan academy
I m a memer
how did he do the last part to verify it?
Y can't I give more than one like😎😎😎😎
Please say the definition of remainder theorem
Sal, why are we plugging in 1 into f(a) and then using that to substitute it into x
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!
@@hisyamhasbi8257 love you man!!!!
How about the exponent??
thankthankthankyouyouyouyouyouyousosososososososososososososmuchmuchmuchmuch!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Sal you also forgot to mention that x=a. Good video tho
i am watching this while online class
you are my best teacher but now day you are not uploading new videos
Is it a -1 or just 1 ????
If f(x) is divided by x-a,remainder= f(a)😊
Polynomial long division....not how I would start my morning lol
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,.......)
f is a function , means f inputs x and outputs a .
I AM THE SMARTEST PERSON NOW
can someone plz tell me what is causing the click sound @ 1:20
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.
No one:
Him: "divisOHr"
😂
APEC LANG MALAKAS HAHAHHA
I was wondering isn't a=-1 ?
"...we deserve a minor drum roll." hahahahha
its morning =
Become my teacher.plz.
But how do you determine the value of a???
It’s where the divisor is
You dont. The value of a is given
It feels like magic
where did f(1) come from?
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!
Sal is goated🫡
It's a little wrong
The remainder is f(x) which is 1 when x-1=0, as a = -1 not 1
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.
Tomorrow's my maths exam...wish me luck!😊☺
What I can I do because is over
yo i know your son he goes to my friends school
what if its ÷ (3x-1)???
I dont know if you still need this but it never does
I was see in 2023
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 .:/
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)
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
It's asking me too find the remainder without using long division 😫😫
Ggs
Yyoyoy
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Dustyn Bennett why are you commenting this stuff on some educational video? go n search for some superstitious stuff and comment
there is no god
I reckon they're just showing their appreciation for this amazing educational content via telling Sal Khan that God and Jesus both love him
Kinda random place for this, no?
Bruh
Khan died for our sins
???
Boring? were's the skip button?
if you already expect us to know how to do it why are you making a video about how to do it.
bro why you talk so slow
So people can understand properly
thank you khan academy