Factor Theorem and Synthetic Division of Polynomial Functions

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This precalculus video tutorial provides a basic introduction into the factor theorem and synthetic division of polynomials.
Introduction to Polynomials: • Polynomials - Classify...
Polynomials - Basic Operations:
• Polynomials - Adding, ...
Dividing Polynomials By Monomials:
• Dividing Polynomials B...
How To Graph Polynomial Functions:
• How To Graph Polynomia...
Intermediate Value Theorem:
• Intermediate Value The...
_____________________________________
Long Division - Polynomials:
• Long Division With Pol...
Polynomial Long Division - More Examples:
• Polynomials - Long Di...
Synthetic Division of Polynomials:
• Synthetic Division of ...
Remainder Theorem & Synthetic Division:
• Remainder Theorem and ...
Factor Theorem & Synthetic Division:
• Factor Theorem and Syn...
Rational Zero Theorem:
• Finding All Zeros of a...
______________________________________
Real & Imaginary Solutions - Polynomials:
• How To Find The Real &...
Solving Polynomial Equations - Synthetic D:
• Solving Polynomial Equ...
Solving Polynomial Equations With Excel:
• Solving Polynomial Equ...
Writing Polynomial Functions Given Zeros:
• Writing Polynomial Fun...
Descartes Rule of Signs:
• Descartes Rule of Signs
Solving Polynomial Inequalities:
• Solving Polynomial Ine...
_____________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Опубликовано:

12 фев 2018

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Комментарии : 244

@TheOrganicChemistryTutor Год назад

Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Iaq7z7reznM.html Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ZTEv8OnGaxo.html Transformations of Functions: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-tyQLp6x-GoU.html Graphing Polynomial Functions: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rOOefdqMvtA.html

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

@joe653 3 года назад

probably a lab coat

@joshuathomas9862 2 года назад

Not all heroes teach maths

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Iron man be like:🤣

@violette6911 3 года назад

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

@sly_ly3632 3 года назад

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@Aidy7 2 года назад

Literally

@bappiahsan2131 8 месяцев назад

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Ikr 😂

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@randall.o8995 5 лет назад

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

@adithiyer9732 4 года назад

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@kesavdarshan 3 года назад

Not underated

@prysm6925 2 года назад

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@bernalesjames9110 2 года назад

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@renameagain5808 2 года назад

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

@TheDarkOne3141 2 года назад

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

@ave9262 5 лет назад

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@omarrasheed3570 3 года назад

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@wroicee3744 3 года назад

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

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@momomai7761 2 года назад

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@Ranjit-kv6yi 2 года назад

Lmfao wtf

@georgesadler7830 2 года назад

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

@ken8771 2 года назад

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 3 года назад

Him still being useful in 2021 🐐

@aigerakabane1312 Год назад

2022 also

@pasohspade6473 9 месяцев назад

2023 too lol

@milkaramos8657 6 месяцев назад

2024 too

@vidhyabayhan6884 Год назад

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

@maeangelipastorfide297 3 года назад

your explanations are so simple, its great

@growgritgive 6 лет назад

Love the content man!

@shuvrachoudhury6963 3 года назад

Better than all other RU-vid videos

@MrEric-rs2wg 2 года назад

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@tristangassil6064 2 года назад

This guy just single-handedly saved my grades

@erwin112000 Год назад

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

@alecescobar9900 2 года назад

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

@sid4931 2 года назад

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

@babygravy7 Год назад

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

@supernova7567 Год назад

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@user-ul3jm2uo7j Год назад

wtf im learning this in grade 8

@11mahekkhan11 10 месяцев назад

@@user-ul3jm2uo7jHow old?

@chynnaroazul4344 2 года назад

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@jackionendino4293 Год назад

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@zippymallows4743 3 года назад

Best teacher...thank you

@9aakshayaprathiba.d418 3 года назад

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

@moshimochi1076 3 года назад

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

@moshimochi1076 3 года назад

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@sandaimeraikage5908 2 года назад

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@olivialeonard5134 2 года назад

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@Backwithanothermilk-HELP_HELPP 4 месяца назад

THIS MAN RIGHT HERE HAS HELPED ME MORE THAN PHOTOMATH

@3kluffy719 4 года назад

Thanks for everything

@uphilldew 3 года назад

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

@AllisLost402 5 лет назад

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@jerichoclemente840 3 года назад

To sacrifice my own life for pakistan

@laleng8862 3 года назад

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@erachan8522 2 года назад

Im loving math rn

@user-mr3wf3xy4t 4 года назад

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 4 года назад

Yep that’s right

@aigerakabane1312 Год назад

That's right

@jennanyquist6284 4 года назад

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?

@mr.habibbi3158 3 года назад

how tf u not verified yet

@shirufaith5625 3 года назад

nice work sir

@abdulhaseeb-sh7oi Год назад

Thank you so much ❤️

@lukathomson3369 3 года назад

Big thanks

@markdavis9990 2 года назад

Any videos on equating coefficients?

@delta25gaming15 3 года назад

im a grade 10 learner and i need help.

@robloxgamermaster4202 9 месяцев назад

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

@LONWABO_R9 3 дня назад

You are the best of the best thank you so much

@ave9262 5 лет назад

Looking forward to high school

@user-ws1wj7ky6k 8 месяцев назад

God blesss you and all that you do ❤

@xo_mics 2 года назад

this is the first time i can't understand it

@jcv.niekerk9848 4 года назад

Thank you

@michaelharveydalen2821 3 года назад

What a genius!...

@Khaled_AbuNawwas21 2 года назад

What a legend !

@WindeSlash 13 дней назад

Respect To You My Bro ❤

@georgie5698 3 года назад

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

@-tweeomoz-1786 Год назад

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 :)

@louislee810 5 месяцев назад

Best teacher

@robosteveny5592 2 года назад

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

@gizerharkshot412 2 года назад

I FINALLY UNDERSTAND

@skye_tnc5679 Год назад

i want to cry every time i learn math.

@josephmagaba378 2 года назад

I just love you.. Life saver

@DimAgozirim 19 дней назад

Thanks so much

@nbastreet8275 Год назад

thanks

@johnnoemartinez8712 3 года назад

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

@user-dh5qn4qn6y Год назад

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?

@tobeymalaugh7826 Год назад

bro is our hero

@JailbreaksHumanebeing 8 месяцев назад

thank you bro

@matthewestrada2205 2 года назад

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

@views-lf9mx 4 года назад

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 :)

@AcekashimaOfficial 8 месяцев назад

Watching this for my exam tommorow, wish me luck 😭

@clli7943 3 года назад

best.

@simpdestroyer5743 2 года назад

bruh, thankyou so much

@Lalaaa62792 4 года назад

How do you find c?

@ahmedel-hindawi9226 4 года назад

my hero

@neillawrence4198 3 года назад

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 2 года назад

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

@3lackman761 Год назад

You're right

@aszpnh1538 11 месяцев назад

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

@aszpnh1538 11 месяцев назад

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

@neillawrence4198 11 месяцев назад

@@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.

@jessicachang3813 Год назад

10:30 thanks again for teaching

@mohdrizwan-hi3dt 2 года назад

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

@frezerabebe4430 8 месяцев назад

Is there anyone watching it again like me😊

@Spu_29 28 дней назад

Tq so much

@aspher_luminous Год назад

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????

@djchilxxn 6 лет назад

you are awesome. i am also jg

@sk-rz8qr 2 года назад

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

@JatPhenshllem 2 года назад

The quadratic equation

@mariamadarboe7894 Год назад

I can't thank you enough but anyway thank you so much I 💗 you.

@_Anna_Nass_ 2 года назад

why is 3 a zero but -3/2 called a root? is it the same thing?

@gdoggx1336 4 года назад

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 3 года назад

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.

@lynnsalee8645 2 года назад

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 2 года назад

i got lost there too 🥺

@Faheem443 2 года назад

@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 2 года назад

@@Faheem443 try it with long division method the answer is different . @souppe i was struck here too.

@Par11ey 2 года назад

x10 times better then my university lectures

@anwarfala2593 Год назад

exactly i accept u

@sinenhlanhlamthembu6671 5 лет назад

what happened to the common factor 2 after factorising ?

@manoelghandour8260 3 года назад

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

@TheDarkOne3141 2 года назад

Maybe he just 4got

@rangareddys1401 3 года назад

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

@tylerschaus9283 3 года назад

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

@reetikarathore56 Год назад

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

@cb2738 Год назад

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 7 месяцев назад

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

@denisecanada3831 5 лет назад

I love your voice. I think I’m in love 💘

@sean4427 5 лет назад

Denise Cañada aw

@icyclestick178 3 года назад

omg a blink LMFAO

@Pulmonary.Tuberculosis 3 года назад

Same his voice is so relaxing

@Animass_editing 3 месяца назад

Can't you do this with multiple variables

@OkoroduduDavid Год назад

GOD WILL BLESS YOUUUUUU😭😭😭😭😭😭

@bwelipitiya78 7 месяцев назад

why is there -2 in the solution for example 1

@syedardhi6049 5 лет назад

How do you find c

@clip_centraI 3 года назад

You're a fucking legend

@keypo790 Год назад

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 Год назад

cubic equation what i mean