Synthetic Division of Polynomials

Рет қаралды 2,966,975

6 жыл бұрын

This precalculus video tutorial provides a basic introduction into synthetic division of polynomials. You can use it to find the quotient and remainder of a division problem with 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

Пікірлер: 1 600

@TheOrganicChemistryTutor Жыл бұрын

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzfaq.info/get/bejne/ppechrVyyquxgmQ.html

@2kchallengewith4video Жыл бұрын

First

@ShroomJGV Жыл бұрын

Damn someone beat me

@vrguy7337 Жыл бұрын

where did you get the 1x that is in your anwser more specificlly why isnt it 1x^2

@hatsuki3846 9 ай бұрын

I love you

@crishajannelvaldez903 8 ай бұрын

@@ShroomJGVqqq

@bubonic_plague_arah747 4 жыл бұрын

me and my three braincells watching this 10 minutes before the test

@fllama 4 жыл бұрын

@@rafav1087 good luck

@rafav1087 4 жыл бұрын

Fardy Alam I got a 60 rip lol, I should have studied

@fllama 4 жыл бұрын

@@rafav1087 ah shit in my last test I failed so u alright

@bubonic_plague_arah747 4 жыл бұрын

update: though 5 months late, i am proud to announce that i failed 🥰🥰 goodnite.

@phoebelin2815 4 жыл бұрын

SAME

@ihaveagunbcuzyes8106 4 жыл бұрын

When you learn more in a 10 minute video than an hour in class

@razormixes6413 4 жыл бұрын

Night of WOLVES fr

@jessicaespinoza627 4 жыл бұрын

so tru

@sabitasahoo5388 4 жыл бұрын

Hey if the subject of your studies deals with maths then why have you kept you channel's name organic chemistry. It is a bit funny.

@akmalr5829 4 жыл бұрын

Same

@honkykongyyankeewitnobrim6220 3 жыл бұрын

my teacher just told us to watch this video for our lesson

@mananite Жыл бұрын

You're literally carrying half of my class, thank you so much

@belindaplanter2230 Жыл бұрын

Can you please help explain the zeroes change in the equation

@eshwar6969 9 ай бұрын

@@belindaplanter2230 equal the denominator to 0 and then do the inver operation to get x= whatever you will get. That I your new denominator

@nour3660 7 ай бұрын

@@belindaplanter2230 the zeros fill in the gaps in the power/exponent, if you have "x^5+x^3/x-2" then there is a missing x^4 and x^1, x^4 after the x^5, and the x^1 is after the x^2, it is just a game or organizing

@abocado121 6 ай бұрын

@@belindaplanter2230if one of the x square or x cube is missing then add 0 to the one who’s missing

@yanalshrooki7616 2 ай бұрын

Why did he become one X square I don’t get that can you explain that better?

@jedthei6099 10 ай бұрын

For anyone (like me) who was confused about why he added a zero to the division table at 6:56: It took some time for me to figure this out too as all of the other explinations of this skipped over this part as well. But basically after playing around with a calculator for a while I figured out the pattern. 7x^3+6x-8 Basically you're counting down from the first "power of" which in this equation is x^3, so using this your next number in the equation would need to fufill x^2 and the next x^1. Since this equations skips directly to x^1 as in 6x, we need to add that placeholder 0 to fufill x^2. 6x fufils x^1 as stated above and we also need to fufill x^0 which the -8 actally does. Another example: 4x^5+4x^2+4 Our highest "power of" in this equation is x^5 so we will be counting down from 5, the next term 4x^2 does not fufil this and since it skips both 4 and 3 we will need to add two zeros. at this point our division table should look like this: 4 0 0 4 next we need to fufil x^1 so we add another 0 and the 4 will fufill x^0 so our table should now look like this: 4 0 0 4 0 4 Hopfully this makes sense, it does to me atleast.

@samuelconsuegra1206 10 ай бұрын

thank you.

@woof6485 10 ай бұрын

super helpful man thank you so much

@Zeus-dh2bn 10 ай бұрын

Tysm❤❤❤❤

@qarashuaq 10 ай бұрын

you saved a lot time for me! thank you very much

@timothybtch1714 10 ай бұрын

Thank you!

@BuysAboveAsk 5 жыл бұрын

better explanation than my college professor

@user-tn1wo4md4n 4 жыл бұрын

Ikr, going into m 2nd test really hope I do well since this vid is basically carrying me

@cosmo8771 4 жыл бұрын

@@user-tn1wo4md4n same lol

@SoraFilms 4 жыл бұрын

Bruh Im at highschool rn and were studying advanced math and calculus

@gagamboy3417 4 жыл бұрын

PoisonedYT same now i am at grade 7

@friskydinngo 4 жыл бұрын

PoisonedYT some of us are dumb

@Lana-or5dz 5 жыл бұрын

I’m taking college Algebra and I love the way you teach Algebra. It’s straight to the point and easy to understand.

@lucykaede5863 4 жыл бұрын

This is you college lesson? Wtf this is my grade 10 lesson 😭

@razormixes6413 4 жыл бұрын

Lucy Kaede damn it’s my 9th grade one

@moondust2365 4 жыл бұрын

@@lucykaede5863 It's my grade 8 lesson. And apparently a grade 7 and 6 lesson too. DepEd is really forcing us to catch up.

@lucykaede5863 4 жыл бұрын

@@moondust2365 Catching up? Nah man this is eating wind already from how advance we are.

@moondust2365 4 жыл бұрын

@@lucykaede5863 I guess so

@mythomaniac9903 6 ай бұрын

You can literally explain the synthetic division of polynomials better in 2 minutes than my math teachers in the past could in an entire class period. It finally clicked. This channel is a godsend, just discovered it now. Wish I had it a few years back in high school.

@briweenie137 3 жыл бұрын

Nothing better than sleeping through class and learning it at 5 am. Definetly makes more sense from you

@Rainjojo 4 жыл бұрын

Since my teacher can’t teach I’m watching this 💀

@jacquellawalker633 4 жыл бұрын

I just don't Understand my teacher AT ALL, SO I COME HERE 😂

@joshhadwiger9390 3 жыл бұрын

FUCKING SAMEEE

@spiffybadger3854 Жыл бұрын

Omg same. My teacher will teach it one day only a little bit then next day quiz.

@sparklingcutie 9 ай бұрын

who ever invented synthetic division must have been irritated by long division

@rexfordluke1480 Ай бұрын

Definitel! 😂

@skunkywild2116 3 жыл бұрын

my teacher: *gives a synthetic division problem* me: but you didn't teach me how to do this organic chemistry tutor: *saves my butt*

@kingkonglee2103 Жыл бұрын

Im so grateful for this kind of channel ,my teacher never taught us in class she just assume we all had learnt it before , youre truly are a lifesaver .

@secret636 3 жыл бұрын

You're such a life-saver! You teach almost every part of the lesson without taking too much time. Looking forward to watching more of your videos. Thank you, Organic Chemistty Tutor!

@mydogsbutcheek 4 жыл бұрын

Want you to know buddy, I am very appreciative of your videos. It isn't just the content, it's they way you make these vids; the way you teach in them. Although for the math vids, it may be easy for me to follow because I took calculus in high school. Now I'm in my freshman year and first semester of college at 26, so it has been a while and I never actually got the college credits for calculus back in high school... now I'm starting back in algebra in college :'(. (though I do have my statistics credits so that's good) The vids I'm most appreciative of is your chemistry vids. That is my one of my intended majors and my teacher doesn't have the best lectures XD. Much love my friend

@scottsmyth1568 2 жыл бұрын

Hey feel free to hit me up for Chem help and this guy is god I am thinking about starting my own channel for bio and chem help

@Just_a_random_person13 2 жыл бұрын

I think I know how you feel. I mean I was a kindergarten teacher, and they threw toys at me during playtime!!!😡🥺😔

@flexicution2323 Жыл бұрын

@@scottsmyth1568 still waiting on them vids bro

@jessejames1520 2 жыл бұрын

These are the best math videos I have ever seen. I love how you explain every detail and point things out so we can follow

@Mr.R_KnowsStuff 4 жыл бұрын

Thank you so much for your videos. Most teachers rush through all the materials they are "required" to cover whether we learn it or not thank you for actually taking the time to explain slowly and thoughtfully. You, sir, are the best.

@gurucharanseva1248 2 жыл бұрын

kzfaq.info/get/bejne/q62YgJhqxM7UZH0.html See video

@mikeecarmona7886 2 жыл бұрын

omg you are a life saver I was literally freaking out when I missed a math class and couldn't understand the notes that were given but this explained EVERYTHING .

@anushkasalvi8811 8 ай бұрын

I cant thank you enough for making these videos and explaining them so well. My teacher doesn't really explain the topics well and rushes through it and the way she teaches it is very confusing. For me, if i need to learn something i need someone to simply explain it to me, like the way you do it. You are literally a life saver for making these videos and explaining the concepts so simply i really appreciate it.

@skylaralison8513 3 жыл бұрын

I love when people explain math and make it simple.. wish everyone could do it like that

@Tom-yh8fj 3 жыл бұрын

My math teacher teach us this when we’re at grade 7 in the Philippines and watching this now when I’m at 10th grade feels nostalgic and still gives me heart attacks in my brain

@GhostLink92 4 жыл бұрын

"I prefer the term artificial separation, myself." Really good stuff. Way better than my professor.

@smart2733 2 жыл бұрын

This is a much more comprehensive explanation than other KZfaq videos I saw, I love it so much

@eagleffgaming7889 4 жыл бұрын

I had many doubts regarding synthetic division. By seeing this video it is easy to do these type of problems. Thank you very much sir.

@br8kspider 3 жыл бұрын

Actually saved me from being behind for possibly the rest of the quarter. Thank you for explaining this better than my teacher ever could

@honeydip8541 5 жыл бұрын

Anybody else tired of seeing that study pug ad?💀

@AMLennon 5 жыл бұрын

driving me crazyyyy

@joeli6509 5 жыл бұрын

Yesss

@taggartknutson1640 5 жыл бұрын

"are the videos from 2009 REALLY helping??" YES! YES THEY ARE! lol

@VicRattlehead1980 5 жыл бұрын

@@taggartknutson1640 ...and the best part about them is that they are free unlike study pug

@taggartknutson1640 5 жыл бұрын

@@VicRattlehead1980 kzfaq.info/get/bejne/edV1mtFy2r3dm3k.html > Megadeth (Ozaka 1995) this is by far the best live performance ive stumbled across caught on video. enjoy ;)

@abegailgarsola2331 4 жыл бұрын

80% of my brain can understand But 20% of my brain cannot understand

@2bkssir108 2 жыл бұрын

Bro if u Nepali then check theach Nepal

@eva677 7 ай бұрын

THANK YOU. I didnt understand the multiplication, adding, and bringing down part since my teacher was going so fast. but how you explaned it makes it make sense. THANK YOU.

@Nemoguzapomnit 6 жыл бұрын

It’s the best solution of that stuff which I ever seen

@chiken9556 2 жыл бұрын

Your videos really helped me study for a test I didn't get notes on because of an absence, thank you!!

@noahmassengill4237 4 жыл бұрын

Dude THANK YOU! You are the only one who has actually explained the 0x^2 thing well, you’re a lifesaver

@terryfoster9050 4 жыл бұрын

From an Aerospace Engineering Major and Current Helicopter Mechanic of 12yrs! Job well done fam! Clear explanation, clear examples, not skipping steps either.... i can dig it

@hidoveconsult7907 Жыл бұрын

You are a wonderful teacher you are carrying all your students along. I wish to be able to teach like you. Thanks for your explanations on all the topics I have viewed.

@Sky_Gazer1 5 жыл бұрын

These video makes the Polynomial division.......... A PIECE OF CAKE!

@CarlPlays60 2 жыл бұрын

Buying skippered that one

@CarlPlays60 2 жыл бұрын

But I skipped that one in my previous one

@zenith8824 2 жыл бұрын

u r cringe dont type

@frostbyte6251 2 жыл бұрын

Agree

@hossderoest9052 3 жыл бұрын

Super duper helpful! Math has always been a struggle, but how you approached teaching this was amazing. Thank you.

@yasmeenah691 Жыл бұрын

Thank you very much for this wonderful presentation of this idea. I am from Jordan 🇯🇴 and I did not understand this idea at all from my teacher, but in this special way things became easier. Thank you from the heart

@kristy_krab_pizza 8 ай бұрын

I’m here because I daydream in class too much 😂😂😂

@augustineo.6990 Жыл бұрын

The simple way you explain it makes all the difference.

@sarahs2376 4 жыл бұрын

I cannot explain how helpful your videos are!!! You are extremely clear. I always use your videos when I need help.

@calypsopendragon5356 5 жыл бұрын

your videos are so helpful for a 10th grader like me

@invok8781 5 жыл бұрын

Same lesson tau hahahaha

@retronex8698 4 жыл бұрын

Hmmm I’m a freshman learning this...

@williamhuynh869 4 жыл бұрын

@@retronex8698 stop flexing please

@fuckywucky9272 4 жыл бұрын

@@retronex8698 I'm a sophomore in college algebra, she might be too. You're probably a freshman in algebra 2 or 1. Not the same thing

@retronex8698 4 жыл бұрын

fucky wucky she said 10th grader...

@berlonjimenez9690 8 ай бұрын

Shout to g10 students who watch this vid for their math lesson

@jishafish5691 3 жыл бұрын

this man actually deserves a nobel peace prize. videos are so useful and easy to understand

@saioofbestboi9008 Жыл бұрын

THANK YOU SO MUCH, I spent an hour confused on these, but you helped me breeze through these!

@PK_Diaspora 3 жыл бұрын

Very good work! It really cleared up some confusion. Thank you for posting such a helpful video.

@fellowbloke741 Жыл бұрын

thank you so much I think about stuff in class that distracts me and I end up missing everything the teacher says, thanks for being my backup

@rohaankhan9018 5 ай бұрын

Man, I literally love this guy. NEVER STOP!

@benkd7521 2 жыл бұрын

you deserve a award , I have been watching you videos since high school , now I'm in uni and I always come here whenever I'm lost in math or physics

@ryomensukuna2147 4 жыл бұрын

I just realized im trying to understand my professor for about 1:30mins in class and still i can hardly solve any of the problem but when this guy explain 10 mins is enough for me to understand the problem

@eriknelson2559 4 жыл бұрын

Awesome explanation! Think that if someone finds the "sign flip" from the factor (e.g. "x-3") to the coefficient in front of the L-bracket (e.g. "+3") confusing, they could use the original number (e.g. "-3") and simply subtract, as per regular long division of polynomials?

@Classicsfrom2023 9 ай бұрын

My dude... without you i would be failing pre calc rn. tysm and keep up the good work. you are the backbone of kids learning math and i hope you get billions more views.

@eyenashfna 3 жыл бұрын

Thank you so much for this. i cannot attend my class that day due to sickness and this vid helped me a lot as i will sit for final tomorrow. may god bless you, you deserved the happiness,wealth and good health.

@girumsolomon9113 Жыл бұрын

What if the divider don't have a real zero ?

@suwilanjisimbule5178 Жыл бұрын

You're way better than my math lecturer thank you so much

@angelinepasigay7524 Жыл бұрын

Your vid really did help me so much. I was struggling how to do my problem as I were reviewing for our exam on Sunday and it really help me solving that one by watching this video. Thank you so much❤️

@sabrinar.2360 4 жыл бұрын

professor been teaching us this for a week straight and i didn’t understand crap. i hop onto this video and i understand it after the first 5 minutes.

@spinzy5990 3 жыл бұрын

This is where I learned how to use the synthetic method. Thank you very much! I have a question, though. What if the divisor has a coefficient of 2 or more?

@xaryabhd2816 5 жыл бұрын

Thanks man. It made me learn the synthetic division in just 10 mins.

@Ravi-pr6fj 3 жыл бұрын

this channel helps more with school than all my math related teachers have combined

@theyoungbarista6715 Жыл бұрын

Thanks again! These videos have helped me out greatly during my time in learning Algebra 2

@tranthamcalhoun3rd432 4 жыл бұрын

Dude Omg if I didn't see this video. I would have lost my mind trying to figure this out

@alanjacob1488 4 жыл бұрын

Frankly, The concept is very easy but teachers somehow manage to twist it up everytime

@1800Kickyodoor Жыл бұрын

bro comes in clutch 20 minutes before the test 😭

@georgesadler7830 2 жыл бұрын

MR. Organic Chemistry Tutor, thank you for an excellent video on Synthetic Division of Polynomials.

@user-jl6rc2vf6z 4 ай бұрын

you're the great lecture who teach all grades I have ever seen

@zoescarborough6958 4 жыл бұрын

oh my gosh, THANK YOU SO MUCH FOR THIS VIDEO YOU SAVED ME

@kal-elbuhay4721 Жыл бұрын

6:44 how do you get the 0x² or how do u know when to add it in the numerator/polynomial?

@stealthcrustyy9487 Жыл бұрын

Don’t know if you still need this since your comment is 2 weeks old but, I’m pretty sure it’s to fill the gap between exponents. In the first example he used it in, the exponents went from 7x^3 to 6x so he used a 0x^2 to “fill the gap”. This is what I’m getting from this.

@mohsenakhavan3500 2 жыл бұрын

Thank you so much. Deeply Appreciated. you describe synthetic division very clearly with different examples. Please keep make videos !

@nizatsongambi5202 2 жыл бұрын

Best explanation I've ever heard, you just make everything easy.

@jashangill4089 4 жыл бұрын

I learnt more Maths from this guy than I did at my school. 🤗

@sunostalgia_9672 5 жыл бұрын

YOU ARE AMAZING! DANG! I UNDERSTOOD IT!!!!! THANK YOU SO MUCH!!!!!!!

@ernykwame4285 3 жыл бұрын

Mr Aderiye if ur reading this i just want u to kno that this man taught me more in 10 min than you could in 1 week

@jordan5688 2 жыл бұрын

I dont know why but his voice makes it so much easier to learn

@minsugavs.yoonki8827 4 жыл бұрын

You've got a nice a voice. Keep teaching. Badly need it 😂

@sabinayasmin7453 4 жыл бұрын

Hey fellow ARMY ✌️ This is my mom’s acc btw so don’t mind the pfp😬

@minsugavs.yoonki8827 4 жыл бұрын

Sabina Yasmin hellloooo. Having trouble with math too? 😂😂

@Valizat 3 жыл бұрын

his voice sounds like those overwatch pros lol

@zenith8824 2 жыл бұрын

ur sus

@rizzzzj 5 жыл бұрын

i love how he writes x

@classycrock 3 жыл бұрын

THANK YOU SO MUCH FOR THIS!! I have a midterm exam tomorrow and I've been trying to figure this out for awhile!!!!!

@wubblyjubbly 2 жыл бұрын

I fail to understand how this will contribute to my life outside of school but I appreciate this video, way better then an hour in my class

@jackluck2538 5 жыл бұрын

This a really helpful video, thanks!

@somerandomstranger1786 2 жыл бұрын

6:36 when and what are the conditions that need to be present to use 0x²?

@sufiserious798 2 жыл бұрын

When you see that a degree of x that should have been present in the continuation is missing, for example an x² should lie in between 7x³ + 6x, if it isn't there then you can go ahead by putting a 0x² in the middle and thus also using it as one of the coefficients while performing synthetic division.

@makalar1643 3 жыл бұрын

I finally understand how to do this and long division of polynomials now because of TOCT. Thank you very much!

@trempire7514 2 жыл бұрын

One of the greatest KZfaq channel I've ever witnessed!!!!

@ericanickerson9819 5 жыл бұрын

I have finals coming up and this was VERY helpful!!!!

@V-oe9cu 3 жыл бұрын

It has been 2 years how are you right now?

@miraekim7609 5 жыл бұрын

THANK YOU FOR UPLOADING THIS VIDEO! IT REALLY HELPED ME!

@HighwayDrive717 4 жыл бұрын

@John Paul G. Atrero next to the x^2

@Ali-uu5pd 3 жыл бұрын

@John Paul Atrero did you figure it out please help me

@mhonthungovung7122 3 жыл бұрын

OMG the best of the best , the way you explain and solve everybody could able to understand easily. Thank you so much for uploading this examples of synthetic division . Love from India ....🌹❤️

@stevennunn 3 жыл бұрын

This video made it very easy to learn synthetic division, thanks very much. Keep up the good work.

@misa4807 4 жыл бұрын

8:00 where did you get the 0 after 7????

@atlantice2659 5 жыл бұрын

I finally understood why you have to put 0 after the number. Arghhh thankyouu you helped me so muuuch :^)

@neblann 4 жыл бұрын

Seriously? Why though?

@moondust2365 4 жыл бұрын

@@neblann It's a place holder like the 0 in 101

@marthabarker8048 2 жыл бұрын

As a retired math teacher who needs a review in order to tutor, this series is great!

@noureldinemam5871 Жыл бұрын

Thank you, thank you, thank you sooo much...2+hrs of trying to learn Polynomials Synthetic Division. and this video just knocked it out for me, had to type this thank you!!

@franckmakosso926 5 жыл бұрын

Thanks again dude you help us a lot.

@shaynerushton214 3 жыл бұрын

I appreciate this tutorial. The solving for x will help me more than I can say. However, I do want to point out, the explanation of why to put the 0 in there when an x of nth degree is missing. like x^3 + 2x + 5. Although I already learned why, but thought I'd point out that deeper explanation would help. Or at least a more in depth reasoning behind why you're doing that.

@sujitsharma5158 3 жыл бұрын

That's because the coefficients of the same degree/order can be added or subtracted

@TheCommandant-wb9tv 2 жыл бұрын

Can you tel me why the fuck they put them zeros when they writing down the numbers that are gonna be divided

@Bhuvan_MS 10 ай бұрын

@@TheCommandant-wb9tv late reply but still, its because coefficients of terms of different powers cannot be subtracted or added directly.

@mysticsummer3573 2 жыл бұрын

this man is the best teacher anyone can ask for.

@mysterypsyche4964 9 ай бұрын

I didn't understand it when my math teacher taught this. But now finally I got it because of this video!

@raunak7488 3 жыл бұрын

tip: if the divisor ax-y has some coefficient a then turn into a unit coefficient i.e. x-y/a

@IAmRustee 3 жыл бұрын

Me after watching OCT's vids at tests: *THIS IS BIG BRAIN TIME.*

@lakshyakumar4882 2 жыл бұрын

This video actually explained this in such an amazing way. Much better than my school book.

@ace.5162 6 ай бұрын

Sse?

@thebegottenwarrior3956 3 жыл бұрын

10 minutes before deadline havent learned synthetic by my module but by you. Thank you for people like you man :DD (especially that if thing about the x - 3 to just flip it my mind couldnt process it but you just made me realize it thanks again :DD)