Factor Theorem and Synthetic Division of Polynomial Functions

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The Organic Chemistry Tutor

The Organic Chemistry Tutor

Күн бұрын

Пікірлер: 266
@TheOrganicChemistryTutor
@TheOrganicChemistryTutor Жыл бұрын
Next Video: kzbin.info/www/bejne/f5LUaK1tp8qtpK8 Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM
@violette6911
@violette6911 4 жыл бұрын
Since we started this module you've been my teacher. Thank you
@sly_ly3632
@sly_ly3632 3 жыл бұрын
Eyyy
@Aidy7
@Aidy7 2 жыл бұрын
Literally
@lemonlizard1
@lemonlizard1 Ай бұрын
he's literally taught me so much math and chemistry this past week it's insane. The only reason I'm keeping up in class
@bappiahsan2131
@bappiahsan2131 Жыл бұрын
I can't thank you enough. You not only helped me pass my maths paper but also got the highest marks.
@jahnabichattopadhyay5972
@jahnabichattopadhyay5972 Ай бұрын
SAME ONG FOR ME TOOO
@adithiyer9732
@adithiyer9732 4 жыл бұрын
Most underrated educational channel ever!
@kesavdarshan
@kesavdarshan 3 жыл бұрын
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@prysm6925
@prysm6925 3 жыл бұрын
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@poggerzloggarz2461 3 жыл бұрын
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@bernalesjames9110
@bernalesjames9110 2 жыл бұрын
cap
@renameagain5808
@renameagain5808 2 жыл бұрын
@@prysm6925 he has 4 million subs, you dumb?
@jakeellul7001
@jakeellul7001 6 жыл бұрын
Not all heroes wear capes
@PremiumDarkChocolate
@PremiumDarkChocolate 4 жыл бұрын
This is so underrated
@animationspace8550
@animationspace8550 3 жыл бұрын
Maybe he wears a cape. We can't see him.
@joe653
@joe653 3 жыл бұрын
probably a lab coat
@joshuathomas9862
@joshuathomas9862 3 жыл бұрын
Not all heroes teach maths
@josephcanzana9092
@josephcanzana9092 3 жыл бұрын
Iron man be like:🤣
@PoppyLophie
@PoppyLophie 3 жыл бұрын
No matter how old these videos will get they are still a life saver for me
@sohamlele8211
@sohamlele8211 4 жыл бұрын
AD : The old youtube maths videos dont help The organic Chemistry tutor : Hold my calculator
@pfeliciano4062
@pfeliciano4062 3 жыл бұрын
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@krishivkaran5337
@krishivkaran5337 3 жыл бұрын
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@ajsh-yx5sd
@ajsh-yx5sd 3 жыл бұрын
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@krishivkaran5337
@krishivkaran5337 3 жыл бұрын
@@ajsh-yx5sd Oh lol
@shadowx3432
@shadowx3432 3 жыл бұрын
Ikr 😂
@randall.o8995
@randall.o8995 5 жыл бұрын
Your explanations are even better than my lecturer ! Damn this is dope.
@TheDarkOne3141
@TheDarkOne3141 3 жыл бұрын
This guys really covers most of the topic for IGCSE. A real big help
@georgesadler7830
@georgesadler7830 2 жыл бұрын
MR. Organic Chemistry Tutor, thank you for a fantastic video on Factor Theorem and Synthetic Division of Polynomial Functions.
@ave9262
@ave9262 5 жыл бұрын
Freshman Calculus is going to be a breeze thanks to you my guy.... g looks
@ken8771
@ken8771 3 жыл бұрын
I didn't understand the explanation of my Prof so I thought it's hard, and came here looking for an easy to understand one, surprisingly it's actually easy. Thanks man.
@rb-plasma4697
@rb-plasma4697 3 жыл бұрын
Him still being useful in 2021 🐐
@Aetherakabane
@Aetherakabane Жыл бұрын
2022 also
@pasohspade6473
@pasohspade6473 Жыл бұрын
2023 too lol
@milkaramos8657
@milkaramos8657 9 ай бұрын
2024 too
@Katatsu7676Satotosu
@Katatsu7676Satotosu Ай бұрын
And soon 2025 also he gonna save me on my college life W goat🐐
@kinet2513
@kinet2513 14 күн бұрын
Yup
@wroicee3744
@wroicee3744 4 жыл бұрын
I just want to marry this guy! His voice is so calming and soothing. Makes you feel you are safe. LOL now lets getto Factor theorem hhh
@SMT1908
@SMT1908 3 жыл бұрын
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@momomai7761
@momomai7761 3 жыл бұрын
his voice makes me feel like everything is going to be okay..
@dancarlodelossantos4759
@dancarlodelossantos4759 3 жыл бұрын
He is the internet dose guy
@Ranjit-kv6yi
@Ranjit-kv6yi 3 жыл бұрын
Lmfao wtf
@fathima5087
@fathima5087 28 күн бұрын
😂
@omarrasheed3570
@omarrasheed3570 3 жыл бұрын
I really hope KZbin blesses you with a high CPM, same way you have blessed us with this educational content.
@maeangelipastorfide297
@maeangelipastorfide297 4 жыл бұрын
your explanations are so simple, its great
@vidhyabayhan6884
@vidhyabayhan6884 Жыл бұрын
Thank you so much It's very useful for me for tomorrow maths exam.🙏🏻🙏🏻
@shuvrachoudhury6963
@shuvrachoudhury6963 3 жыл бұрын
Better than all other KZbin videos
@alecescobar9900
@alecescobar9900 2 жыл бұрын
Stuff's pretty complicated, but preparing beforehand so I don't fail grade 12 functions. Thanks this channel is the best.
@sid4931
@sid4931 2 жыл бұрын
ur learning this in grade 12? Im learning in grade 10, thought this was supp to be lower grade stuff
@babygravy7
@babygravy7 2 жыл бұрын
@@sid4931 congrats. Some people don’t learn as quickly as you do. Maybe consider that next time
@supernova7567
@supernova7567 2 жыл бұрын
@@sid4931 Would you like a cookie?
@vyombhatnagar-v8u
@vyombhatnagar-v8u Жыл бұрын
wtf im learning this in grade 8
@11mahekkhan11
@11mahekkhan11 Жыл бұрын
​@@vyombhatnagar-v8uHow old?
@olivialeonard5134
@olivialeonard5134 2 жыл бұрын
thanks for taking it slow and explaining throughly and clearly I really really appreciate it!!
@uphilldew
@uphilldew 3 жыл бұрын
big thanks for you,sir,i was planning to study for my medical college entrance exam,but i'm still in grade 10,and your videos really help me,thanks a lot
@tristangassil6064
@tristangassil6064 3 жыл бұрын
This guy just single-handedly saved my grades
@thisisavivistanaccount7866
@thisisavivistanaccount7866 19 күн бұрын
this is old but you saved me!! I was damn near sobbing trying to figure out how to do this
@AllisLost402
@AllisLost402 5 жыл бұрын
you are the best teacher i have ever had love from Pakistan!
@jerichoclemente840
@jerichoclemente840 4 жыл бұрын
To sacrifice my own life for pakistan
@laleng8862
@laleng8862 4 жыл бұрын
@@jerichoclemente840.
@-tweeomoz-1786
@-tweeomoz-1786 Жыл бұрын
This has got to be the most tedious genre of math we've had to do so far; usually, algebra is so fun, but these problems just drag on. Thanks for the video, really helped with my comprehension :)
@erwin112000
@erwin112000 Жыл бұрын
this man makes a 1 hour lecture into the same thing but simplified, Easier to understand, and takes 16.67% from that usual 1 hour (It is 10 mins than the usual 60 mins
@JesmineIrai-hs9pg
@JesmineIrai-hs9pg 2 ай бұрын
For sure
@MrEric-rs2wg
@MrEric-rs2wg 3 жыл бұрын
Your videos honestly helps me a lot
@growgritgive
@growgritgive 6 жыл бұрын
Love the content man!
@robloxgamermaster4202
@robloxgamermaster4202 Жыл бұрын
I have a bunch of hw due and a professor that can’t teach. This guys a lifesaver
@JerickZhang
@JerickZhang 13 күн бұрын
Chemistry tutor has changed my life
@jackionendino4293
@jackionendino4293 2 жыл бұрын
Thnaks alot 🥺❤️really helps me get on the move
@neillawrence4198
@neillawrence4198 4 жыл бұрын
The last example is not correct. If you multiply (2x+3) times (12x^2 - 2x - 2) as shown in bottom right at about 7:30, you do not get back to the original expression. The factor (2x+3) should be left as (x + 3/2). (x + 3/2) times (12x^2 -2x - 2) = (12x^3 + 16x^2 - 5x -3) the original expression. However, if you ignore and continue to factor, you do end up with the same final three solutions. Back two years later to edit. (12/29/23) To clarify, the equality statement at 7:30 as stated is not correct. Expanding the equality as shown gives a result off by a factor of 2. Eliminating the fraction from (x+3/2) introduces a factor of 2 into things. He later factors this out of the polynomial, then removes completly by dividing both sides of the equality by 2. Where this 2 came from and what happened to it he never explained.
@yesimkhanh9932
@yesimkhanh9932 3 жыл бұрын
yeah, lol, i was thinking about the exactly same thing
@3lackman761
@3lackman761 Жыл бұрын
You're right
@aszpnh1538
@aszpnh1538 Жыл бұрын
LOL HE did explain it. Notice he took out a two when factoring 12x^2 - 2 x -2
@aszpnh1538
@aszpnh1538 Жыл бұрын
He basically just multiplied the whole expression by 2 on both sides willing doesn’t change the value. Please understand this.
@neillawrence4198
@neillawrence4198 Жыл бұрын
@@aszpnh1538 I do fully understand. What he did to eliminate the fraction by introducing a factor of two, then factoring out later in the final solution is perfectly fine, and I most likely would have done that myself. What I am pointing out is that the equality shown at the bottom at 7:30 IS NOT EQUAL. The left side does not have the factor of two, the right side includes the factor of two. If you foil the right side you do not get the left side, therefore the two cannot be shown as equal. The left side needs to be shown as (2)(12x^3+16x^2-5x-3) in order for the equality to be true. He did say what he was doing in each step, but someone just getting into this may not follow. When he removed the factor of two it would help others if he remarked he was removing the factor of two that he had introduced earlier. OK, nuff said, I'm done.
@chynnaroazul4344
@chynnaroazul4344 2 жыл бұрын
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@sandaimeraikage5908
@sandaimeraikage5908 3 жыл бұрын
Bro you drop this!:👑
@user-mr3wf3xy4t
@user-mr3wf3xy4t 4 жыл бұрын
So Remainder Theorem tells us that the remainder is always equal to f(c). And Factor Theorem tells us that if the remainder is 0, then the smaller polynomial is a factor of the other. Is that it? Or no?
@thef.b.i2705
@thef.b.i2705 4 жыл бұрын
Yep that’s right
@Aetherakabane
@Aetherakabane Жыл бұрын
That's right
@ChetanSaiP
@ChetanSaiP 2 ай бұрын
Thank you for saving me on this topic and my exam is about to start in 1hour😅
@zippymallows4743
@zippymallows4743 3 жыл бұрын
Best teacher...thank you
@views-lf9mx
@views-lf9mx 4 жыл бұрын
Correct me if I am wrong but I think you are doing the vieta formula wrong and it is not the first video. For ex 3:20 you say the product of the zeros are -2 and they add to negative one. That is wrong because they add to +1 ( formula x1+x2= -b/a => -(-1)/1=+1 and product x1*x2=c/a => -2/1=-2.) So this means x´2-x-2 is not equal to (x-2)(x+1). The zeros are -2 and 1 and the equation is a product of (x+2)(x-1). Anyway thnx for all the tutorials in general they are really helpful :)
@georgie5698
@georgie5698 3 жыл бұрын
I would of never picked this subject if I knew my teacher was gonna be 70 with a harsh Indian accent. I have to watch this guys videos after every lesson and do the whole this again
@erachan8522
@erachan8522 2 жыл бұрын
Im loving math rn
@moshimochi1076
@moshimochi1076 4 жыл бұрын
6:15 thats a terrible looking 3 HJKSAH i was so tired and then PFFT-- thank you for waking me up
@moshimochi1076
@moshimochi1076 4 жыл бұрын
i just made the comments 69 oof
@jahnabichattopadhyay5972
@jahnabichattopadhyay5972 Ай бұрын
this is life saver
@robosteveny5592
@robosteveny5592 2 жыл бұрын
Thank you I will pass my exam now I hope :>
@skye_tnc5679
@skye_tnc5679 2 жыл бұрын
i want to cry every time i learn math.
@WindeSlash
@WindeSlash 3 ай бұрын
Respect To You My Bro ❤
@markdavis9990
@markdavis9990 2 жыл бұрын
Any videos on equating coefficients?
@strawberryme16
@strawberryme16 3 жыл бұрын
this is the first time i can't understand it
@jennanyquist6284
@jennanyquist6284 4 жыл бұрын
I thought you found the factor of the quotient by finding what multiplied to ac and added to b. Is it different for synthetic division?
@abdulhaseeb-sh7oi
@abdulhaseeb-sh7oi 2 жыл бұрын
Thank you so much ❤️
@9aakshayaprathiba.d418
@9aakshayaprathiba.d418 4 жыл бұрын
My exam fear gone by seeing this video .......thank you :D LOL
@mr.habibbi3158
@mr.habibbi3158 4 жыл бұрын
how tf u not verified yet
@DianaWinters-y2h
@DianaWinters-y2h 11 ай бұрын
God blesss you and all that you do ❤
@LONWABO_R9
@LONWABO_R9 3 ай бұрын
You are the best of the best thank you so much
@shirufaith5625
@shirufaith5625 4 жыл бұрын
nice work sir
@tobeymalaugh7826
@tobeymalaugh7826 2 жыл бұрын
bro is our hero
@delta25gaming15
@delta25gaming15 3 жыл бұрын
im a grade 10 learner and i need help.
@lukathomson3369
@lukathomson3369 3 жыл бұрын
Big thanks
@michaelharveydalen2821
@michaelharveydalen2821 4 жыл бұрын
What a genius!...
@matthewestrada2205
@matthewestrada2205 2 жыл бұрын
im gonna watch this everyday until i get it , trust the process !!!!!
@ave9262
@ave9262 5 жыл бұрын
Looking forward to high school
@Khaled_AbuNawwas21
@Khaled_AbuNawwas21 2 жыл бұрын
What a legend !
@louislee810
@louislee810 9 ай бұрын
Best teacher
@frezerabebe4430
@frezerabebe4430 11 ай бұрын
Is there anyone watching it again like me😊
@AcekashimaOfficial
@AcekashimaOfficial 11 ай бұрын
Watching this for my exam tommorow, wish me luck 😭
@Par11ey
@Par11ey 2 жыл бұрын
x10 times better then my university lectures
@anwarfala2593
@anwarfala2593 Жыл бұрын
exactly i accept u
@gizerharkshot412
@gizerharkshot412 3 жыл бұрын
I FINALLY UNDERSTAND
@OkoroduduDavid
@OkoroduduDavid Жыл бұрын
GOD WILL BLESS YOUUUUUU😭😭😭😭😭😭
@keypo790
@keypo790 Жыл бұрын
So its like, plugging in different numbers and waiting until zero comes out, so that there we can easily use synthethic division to get the factors of the polynomials, OR by using quadratic formula to find that value of x.
@keypo790
@keypo790 Жыл бұрын
cubic equation what i mean
@sk-rz8qr
@sk-rz8qr 2 жыл бұрын
if the last factor cannot be factored further for example: x^2-5x+12, what do you do?
@JatPhenshllem
@JatPhenshllem 2 жыл бұрын
The quadratic equation
@dv4346
@dv4346 5 жыл бұрын
everyone's always praising this guy but to me it just sounds like he's about to cry
@FHD80057
@FHD80057 5 жыл бұрын
who cares what he sounds like
@dv4346
@dv4346 5 жыл бұрын
@@FHD80057 I mean when you're trying to understand a concept it is lol. It might not be important for some people but it most definitely is for teachers what they sound like.
@ahmedel-hindawi9226
@ahmedel-hindawi9226 5 жыл бұрын
maybe
@azyle2104
@azyle2104 4 жыл бұрын
@@dv4346 idk what's your issue with his voice
@azyle2104
@azyle2104 4 жыл бұрын
Probably an underachiever
@EdohoEric
@EdohoEric Жыл бұрын
Great video but what happens to the (2) at the end of the video, after equating the rest to zero and getting their respective value for x what happens to the (2) amongst them?
@gdoggx1336
@gdoggx1336 4 жыл бұрын
But what would you do if in question 1 they didn’t tell you if 3 was a 0 of f(x). And what would you do if they didn’t tell you -3/2 was your root in the second equation. I’m trying to do this but in my questions they don’t give you a hint or straight out tell you was f(x) is. They just give me a polynomial equal to zero and ask me to factor. Please help, thanks.
@delinaberhane1963
@delinaberhane1963 4 жыл бұрын
Gdogg x13 you graph the equation in desmos I don’t know if you know about desmos. But it is actually a website that you can use to graph.and then you look at the point where it cross the x axis I hope this helps.
@johnnoemartinez8712
@johnnoemartinez8712 4 жыл бұрын
Can you please try to solve polynomial function in synthetic division with a reminder is more than 1.
@foufou3616
@foufou3616 Ай бұрын
help!! if we look at the equality at 10:33 on the bottom, and graph both sides, you'll see that (2x+3)(2)(2x-1)(3x+1) is bigger by a factor of two than 12x^3+16x^2--5x-3, when i factorized this equation myself i used the given zero f(-3/2)=0 to to find the following factor: x=-3/2, (x+3/2)=0. not (2x+3). the roots remain the same but if this equation will be used to find any other value that isn't a zero, it will be wrong, how can we ensure that we dont factorize wrongly without using a graphing calculator? thank you in advance
@kerubifimanekapohamba4001
@kerubifimanekapohamba4001 11 ай бұрын
Solve the following equation for me please using factor theorem..in this situation no factor provided. 1. 2x³-7x²+2x+3=0 2. 6x3+19x²+x-6=0
@ChanithDinayana
@ChanithDinayana 2 ай бұрын
Thank you❤
@3kluffy719
@3kluffy719 4 жыл бұрын
Thanks for everything
@reetikarathore56
@reetikarathore56 2 жыл бұрын
For the first example, how did 4x^2 become 1x when factored by x?
@cb2738
@cb2738 2 жыл бұрын
2:18 Take a closer look; -4 + 3 = -1 Then x^2 becomes x, because we are taking away an x when we divided the entire equation by (x-3) Hope it helps
@bwelipitiya78
@bwelipitiya78 10 ай бұрын
so how x become -2 in the first example? @@cb2738
@DimAgozirim
@DimAgozirim 3 ай бұрын
Thanks so much
@jessicachang3813
@jessicachang3813 2 жыл бұрын
10:30 thanks again for teaching
@rangareddys1401
@rangareddys1401 4 жыл бұрын
How do you know that you should take x-3? Why can’t you take other number???
@tylerschaus9283
@tylerschaus9283 3 жыл бұрын
because the question started that 3 was a 0 meaning it is an x intercept or x value of the graph. he already knew that it was divisible by x-3 he was just doing it to show the process. don’t know if u need this anymore but that’s it
@clli7943
@clli7943 3 жыл бұрын
best.
@teteria8414
@teteria8414 Ай бұрын
Math Jesus May you give us hope for our upcoming exam
@MicaF.P
@MicaF.P Ай бұрын
When solving a factor of theorem you'll use synthetic division???
@nbastreet8275
@nbastreet8275 Жыл бұрын
thanks
@aspher_luminous
@aspher_luminous Жыл бұрын
What if the polynomial has a remainder when using the synthetic division, can you still use factor theorem if the sythetic divison used to the polynomial has a remainder????
@josephmagaba378
@josephmagaba378 3 жыл бұрын
I just love you.. Life saver
@TheAshleyZixuan
@TheAshleyZixuan 3 жыл бұрын
The last question is wrong
@haythamahmed4144
@haythamahmed4144 6 ай бұрын
I'm literally watching this in the middle of an irl horrible teacher class
@mohdrizwan-hi3dt
@mohdrizwan-hi3dt 2 жыл бұрын
How you set up every thing for making this videos any help please
@lynnsalee8645
@lynnsalee8645 3 жыл бұрын
I was kinda lost at 2:10 - 2:16 when we were factoring the x ( in the factor (x - 3) ) in the whole function, how did we arrive to 1x^2-1x-2 especially the -2 part I was lost. Anybody who understood??🤔🤔
@souppe9616
@souppe9616 3 жыл бұрын
i got lost there too 🥺
@Sf08321
@Sf08321 2 жыл бұрын
@Lynn Salee Essentially, the answers from the synthetic division are: 1, -1 and -2 so you have to substitute the numbers into the equation so you get 1x^2-1x-2 We get -2 from 1-3=-2
@falgunsharma6508
@falgunsharma6508 2 жыл бұрын
@@Sf08321 try it with long division method the answer is different . @souppe i was struck here too.
@lilpogchamp4904
@lilpogchamp4904 3 жыл бұрын
Me in his videos be like: yes officer
@JailbreaksHumanebeing
@JailbreaksHumanebeing Жыл бұрын
thank you bro
@sinenhlanhlamthembu6671
@sinenhlanhlamthembu6671 5 жыл бұрын
what happened to the common factor 2 after factorising ?
@manoelghandour8260
@manoelghandour8260 4 жыл бұрын
I don't know he neglected it I think he should have distributed it by multiplying it by each bracket.
@TheDarkOne3141
@TheDarkOne3141 3 жыл бұрын
Maybe he just 4got
@Spu_29
@Spu_29 4 ай бұрын
Tq so much
@solo_gamin2
@solo_gamin2 10 ай бұрын
5:03 the -3/2 would be converted to +3/2
@maikahbucay895
@maikahbucay895 3 жыл бұрын
This is a fact, i forgot my lessons in grade 8, that's why i cant understand a thing. LOL, EVERYTHING IS CONNECTED!!!!!! (i feel like, i need to rewind my lessons in grade 8 before i continue this lessons)
@jcv.niekerk9848
@jcv.niekerk9848 4 жыл бұрын
Thank you
@Lalaaa62792
@Lalaaa62792 4 жыл бұрын
How do you find c?
@RajvardhanSingh-nv6lw
@RajvardhanSingh-nv6lw Жыл бұрын
DHATT MARDAWA 😊
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