Factor Theorem and Synthetic Division of Polynomial Functions

[@TheOrganicChemistryTutor]

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]

Since we started this module you've been my teacher. Thank you

[@sly_ly3632]

Eyyy

[@Aidy7]

Literally

[@lemonlizard1]

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]

I can't thank you enough. You not only helped me pass my maths paper but also got the highest marks.

[@jahnabichattopadhyay5972]

SAME ONG FOR ME TOOO

[@adithiyer9732]

Most underrated educational channel ever!

[@kesavdarshan]

Not underated

[@prysm6925]

@@kesavdarshan underrated

[@poggerzloggarz2461]

@@prysm6925 well rated

[@bernalesjames9110]

cap

[@renameagain5808]

@@prysm6925 he has 4 million subs, you dumb?

[@jakeellul7001]

Not all heroes wear capes

[@PremiumDarkChocolate]

This is so underrated

[@animationspace8550]

Maybe he wears a cape. We can't see him.

[@joe653]

probably a lab coat

[@joshuathomas9862]

Not all heroes teach maths

[@josephcanzana9092]

Iron man be like:🤣

[@PoppyLophie]

No matter how old these videos will get they are still a life saver for me

[@sohamlele8211]

AD : The old youtube maths videos dont help The organic Chemistry tutor : Hold my calculator

[@pfeliciano4062]

Hahahshhshshshshshshshshshshhshahahahahhahahahshsh😂😂😂😂😂😂😂😂😂

[@krishivkaran5337]

AD?

[@ajsh-yx5sd]

@@krishivkaran5337 advertisement.

[@krishivkaran5337]

@@ajsh-yx5sd Oh lol

[@shadowx3432]

Ikr 😂

[@randall.o8995]

Your explanations are even better than my lecturer ! Damn this is dope.

[@TheDarkOne3141]

This guys really covers most of the topic for IGCSE. A real big help

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a fantastic video on Factor Theorem and Synthetic Division of Polynomial Functions.

[@ave9262]

Freshman Calculus is going to be a breeze thanks to you my guy.... g looks

[@ken8771]

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]

Him still being useful in 2021 🐐

[@Aetherakabane]

2022 also

[@pasohspade6473]

2023 too lol

[@milkaramos8657]

2024 too

[@Katatsu7676Satotosu]

And soon 2025 also he gonna save me on my college life W goat🐐

[@kinet2513]

Yup

[@wroicee3744]

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]

Back off Wroi HES MINE!!!!!!!!!!!!

[@momomai7761]

his voice makes me feel like everything is going to be okay..

[@dancarlodelossantos4759]

He is the internet dose guy

[@Ranjit-kv6yi]

Lmfao wtf

[@fathima5087]

😂

[@omarrasheed3570]

I really hope KZbin blesses you with a high CPM, same way you have blessed us with this educational content.

[@maeangelipastorfide297]

your explanations are so simple, its great

[@vidhyabayhan6884]

Thank you so much It's very useful for me for tomorrow maths exam.🙏🏻🙏🏻

[@shuvrachoudhury6963]

Better than all other KZbin videos

[@alecescobar9900]

Stuff's pretty complicated, but preparing beforehand so I don't fail grade 12 functions. Thanks this channel is the best.

[@sid4931]

ur learning this in grade 12? Im learning in grade 10, thought this was supp to be lower grade stuff

[@babygravy7]

@@sid4931 congrats. Some people don’t learn as quickly as you do. Maybe consider that next time

[@supernova7567]

@@sid4931 Would you like a cookie?

[@vyombhatnagar-v8u]

wtf im learning this in grade 8

[@11mahekkhan11]

​@@vyombhatnagar-v8uHow old?

[@olivialeonard5134]

thanks for taking it slow and explaining throughly and clearly I really really appreciate it!!

[@uphilldew]

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]

This guy just single-handedly saved my grades

[@thisisavivistanaccount7866]

this is old but you saved me!! I was damn near sobbing trying to figure out how to do this

[@AllisLost402]

you are the best teacher i have ever had love from Pakistan!

[@jerichoclemente840]

To sacrifice my own life for pakistan

[@laleng8862]

@@jerichoclemente840.

[@-tweeomoz-1786]

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]

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]

For sure

[@MrEric-rs2wg]

Your videos honestly helps me a lot

[@growgritgive]

Love the content man!

[@robloxgamermaster4202]

I have a bunch of hw due and a professor that can’t teach. This guys a lifesaver

[@JerickZhang]

Chemistry tutor has changed my life

[@jackionendino4293]

Thnaks alot 🥺❤️really helps me get on the move

[@neillawrence4198]

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]

yeah, lol, i was thinking about the exactly same thing

[@3lackman761]

You're right

[@aszpnh1538]

LOL HE did explain it. Notice he took out a two when factoring 12x^2 - 2 x -2

[@aszpnh1538]

He basically just multiplied the whole expression by 2 on both sides willing doesn’t change the value. Please understand this.

[@neillawrence4198]

@@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]

Man I love you so much I can easily understand you in a short period of time 💙🧡💚

[@sandaimeraikage5908]

Bro you drop this!:👑

[@user-mr3wf3xy4t]

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]

Yep that’s right

[@Aetherakabane]

That's right

[@ChetanSaiP]

Thank you for saving me on this topic and my exam is about to start in 1hour😅

[@zippymallows4743]

Best teacher...thank you

[@views-lf9mx]

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]

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]

Im loving math rn

[@moshimochi1076]

6:15 thats a terrible looking 3 HJKSAH i was so tired and then PFFT-- thank you for waking me up

[@moshimochi1076]

i just made the comments 69 oof

[@jahnabichattopadhyay5972]

this is life saver

[@robosteveny5592]

Thank you I will pass my exam now I hope :>

[@skye_tnc5679]

i want to cry every time i learn math.

[@WindeSlash]

Respect To You My Bro ❤

[@markdavis9990]

Any videos on equating coefficients?

[@strawberryme16]

this is the first time i can't understand it

[@jennanyquist6284]

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]

Thank you so much ❤️

[@9aakshayaprathiba.d418]

My exam fear gone by seeing this video .......thank you :D LOL

[@mr.habibbi3158]

how tf u not verified yet

[@DianaWinters-y2h]

God blesss you and all that you do ❤

[@LONWABO_R9]

You are the best of the best thank you so much

[@shirufaith5625]

nice work sir

[@tobeymalaugh7826]

bro is our hero

[@delta25gaming15]

im a grade 10 learner and i need help.

[@lukathomson3369]

Big thanks

[@michaelharveydalen2821]

What a genius!...

[@matthewestrada2205]

im gonna watch this everyday until i get it , trust the process !!!!!

[@ave9262]

Looking forward to high school

[@Khaled_AbuNawwas21]

What a legend !

[@louislee810]

Best teacher

[@frezerabebe4430]

Is there anyone watching it again like me😊

[@AcekashimaOfficial]

Watching this for my exam tommorow, wish me luck 😭

[@Par11ey]

x10 times better then my university lectures

[@anwarfala2593]

exactly i accept u

[@gizerharkshot412]

I FINALLY UNDERSTAND

[@OkoroduduDavid]

GOD WILL BLESS YOUUUUUU😭😭😭😭😭😭

[@keypo790]

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]

cubic equation what i mean

[@sk-rz8qr]

if the last factor cannot be factored further for example: x^2-5x+12, what do you do?

[@JatPhenshllem]

The quadratic equation

[@dv4346]

everyone's always praising this guy but to me it just sounds like he's about to cry

[@FHD80057]

who cares what he sounds like

[@dv4346]

@@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]

maybe

[@azyle2104]

@@dv4346 idk what's your issue with his voice

[@azyle2104]

Probably an underachiever

[@EdohoEric]

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]

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]

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]

Can you please try to solve polynomial function in synthetic division with a reminder is more than 1.

[@foufou3616]

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]

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]

Thank you❤

[@3kluffy719]

Thanks for everything

[@reetikarathore56]

For the first example, how did 4x^2 become 1x when factored by x?

[@cb2738]

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]

so how x become -2 in the first example? @@cb2738

[@DimAgozirim]

Thanks so much

[@jessicachang3813]

10:30 thanks again for teaching

[@rangareddys1401]

How do you know that you should take x-3? Why can’t you take other number???

[@tylerschaus9283]

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]

best.

[@teteria8414]

Math Jesus May you give us hope for our upcoming exam

[@MicaF.P]

When solving a factor of theorem you'll use synthetic division???

[@nbastreet8275]

thanks

[@aspher_luminous]

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]

I just love you.. Life saver

[@TheAshleyZixuan]

The last question is wrong

[@haythamahmed4144]

I'm literally watching this in the middle of an irl horrible teacher class

[@mohdrizwan-hi3dt]

How you set up every thing for making this videos any help please

[@lynnsalee8645]

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]

i got lost there too 🥺

[@Sf08321]

@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]

@@Sf08321 try it with long division method the answer is different . @souppe i was struck here too.

[@lilpogchamp4904]

Me in his videos be like: yes officer

[@JailbreaksHumanebeing]

thank you bro

[@sinenhlanhlamthembu6671]

what happened to the common factor 2 after factorising ?

[@manoelghandour8260]

I don't know he neglected it I think he should have distributed it by multiplying it by each bracket.

[@TheDarkOne3141]

Maybe he just 4got

[@Spu_29]

Tq so much

[@solo_gamin2]

5:03 the -3/2 would be converted to +3/2

[@maikahbucay895]

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]

Thank you

[@Lalaaa62792]

How do you find c?

[@RajvardhanSingh-nv6lw]

DHATT MARDAWA 😊