Synthetic Division of Polynomials
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- Опубликовано: 2 окт 2024
- 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-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/p1lSRAeEMR0/видео.html
First
Damn someone beat me
where did you get the 1x that is in your anwser more specificlly why isnt it 1x^2
I love you
@@ShroomJGVqqq
You're literally carrying half of my class, thank you so much
Can you please help explain the zeroes change in the equation
@@belindaplanter2230 equal the denominator to 0 and then do the inver operation to get x= whatever you will get. That I your new denominator
@@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
@@belindaplanter2230if one of the x square or x cube is missing then add 0 to the one who’s missing
Why did he become one X square I don’t get that can you explain that better?
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.
like bro really an hour siting in the class for the whole period listening to the teacher explaining maths and synthetic division cant suffice the time u watch JG explain all of this in 10 minutes and now we understand the hour period in class just ruins your attention span really .But we got JG n he cooked here in this video I mean look at the million views just proves his king😁😭😭💯🔥
me and my three braincells watching this 10 minutes before the test
@@rafav1087 good luck
Fardy Alam I got a 60 rip lol, I should have studied
@@rafav1087 ah shit in my last test I failed so u alright
update: though 5 months late, i am proud to announce that i failed 🥰🥰 goodnite.
SAME
who ever invented synthetic division must have been irritated by long division
Definitel! 😂
I’m taking college Algebra and I love the way you teach Algebra. It’s straight to the point and easy to understand.
This is you college lesson? Wtf this is my grade 10 lesson 😭
Lucy Kaede damn it’s my 9th grade one
@@lucykaede5863 It's my grade 8 lesson. And apparently a grade 7 and 6 lesson too. DepEd is really forcing us to catch up.
@@moondust2365 Catching up? Nah man this is eating wind already from how advance we are.
@@lucykaede5863 I guess so
Nothing better than sleeping through class and learning it at 5 am. Definetly makes more sense from you
When you learn more in a 10 minute video than an hour in class
Night of WOLVES fr
so tru
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.
Same
my teacher just told us to watch this video for our lesson
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 .
better explanation than my college professor
Ikr, going into m 2nd test really hope I do well since this vid is basically carrying me
@@user-tn1wo4md4n same lol
Bruh Im at highschool rn and were studying advanced math and calculus
PoisonedYT same now i am at grade 7
PoisonedYT some of us are dumb
my teacher: *gives a synthetic division problem*
me: but you didn't teach me how to do this
organic chemistry tutor: *saves my butt*
Since my teacher can’t teach I’m watching this 💀
I just don't Understand my teacher AT ALL, SO I COME HERE 😂
FUCKING SAMEEE
Omg same. My teacher will teach it one day only a little bit then next day quiz.
SAMEEE
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.
thank you.
super helpful man thank you so much
Tysm❤❤❤❤
you saved a lot time for me! thank you very much
Thank you!
Anybody else tired of seeing that study pug ad?💀
driving me crazyyyy
Yesss
"are the videos from 2009 REALLY helping??" YES! YES THEY ARE! lol
@@taggartknutson1640 ...and the best part about them is that they are free unlike study pug
@@VicRattlehead1980 ruclips.net/video/CoEgnAuWykE/видео.html > Megadeth (Ozaka 1995) this is by far the best live performance ive stumbled across caught on video. enjoy ;)
"I prefer the term artificial separation, myself."
Really good stuff. Way better than my professor.
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
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
I think I know how you feel. I mean I was a kindergarten teacher, and they threw toys at me during playtime!!!😡🥺😔
@@scottsmyth1568 still waiting on them vids bro
I love when people explain math and make it simple.. wish everyone could do it like that
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
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.
These video makes the Polynomial division.......... A PIECE OF CAKE!
Buying skippered that one
But I skipped that one in my previous one
u r cringe dont type
Agree
80% of my brain can understand
But
20% of my brain cannot understand
Bro if u Nepali then check theach Nepal
The simple way you explain it makes all the difference.
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.
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!
all love from south africa man ❣😊.Bro deserves an award cause now i fully understand the synthetic division method u really helped me , u r the best person to explain such complex math problems we face but by u .U made maths easier 💯
I cannot explain how helpful your videos are!!! You are extremely clear. I always use your videos when I need help.
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❤️
You're way better than my math lecturer thank you so much
These help so much I feel like I have to teach myself all my work and these help so much
You've got a nice a voice. Keep teaching. Badly need it 😂
Hey fellow ARMY ✌️
This is my mom’s acc btw so don’t mind the pfp😬
Sabina Yasmin hellloooo. Having trouble with math too? 😂😂
his voice sounds like those overwatch pros lol
ur sus
One of the greatest RUclips channel I've ever witnessed!!!!
I’m here because I daydream in class too much 😂😂😂
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
Shout to g10 students who watch this vid for their math lesson
you explained something in 10 minutes that took my teacher 90 minutes to explain. thank you
It’s the best solution of that stuff which I ever seen
Please kindly call yourself the universal teacher. This guy is a genius
Dude Omg if I didn't see this video. I would have lost my mind trying to figure this out
Frankly, The concept is very easy but teachers somehow manage to twist it up everytime
As a retired math teacher who needs a review in order to tutor, this series is great!
i love how he writes x
this is such a clutch, im gonna have my second quarter examination for algebra tom. This is such a win!
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.
That's because the coefficients of the same degree/order can be added or subtracted
Can you tel me why the fuck they put them zeros when they writing down the numbers that are gonna be divided
@@TheCommandant-wb9tv late reply but still, its because coefficients of terms of different powers cannot be subtracted or added directly.
This really helped me lol since I'm at grade 10 and since I was absent on our math class and the professor wouldn't even tell me how to do it. Thank you so much for making this video even though its already 6 years ago. I understood it better than our strict professor lol, I hope this guy is my prof😂
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.
ruclips.net/video/uGhM59_hp4I/видео.html
See video
This video actually explained this in such an amazing way. Much better than my school book.
Sse?
your videos are so helpful for a 10th grader like me
Same lesson tau hahahaha
Hmmm I’m a freshman learning this...
@@retronex8698 stop flexing please
@@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
fucky wucky she said 10th grader...
got a test that will make or break my grade tmr, thank you so much for this.
oh my gosh, THANK YOU SO MUCH FOR THIS VIDEO YOU SAVED ME
Saved me. Tomorrow's a 30 mark test on this and some other stuff.
THANK YOU SOOO MUCH!!!!
6:44 how do you get the 0x² or how do u know when to add it in the numerator/polynomial?
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.
thank you for helping me prepare for my finals. your videos have saved me many times
bruh i swear my teacher doesnt even have a highschool degree, ive spent more time on youtube learning this stuff than in her class
It’s videos like these that make me realize I like math, just hate how stressful it is when you don’t have a well suited teacher that makes it comprehendible.
What if the divider don't have a real zero ?
To anyone confused why there are zeros:
A polynomial function is defined as f(x) = aₙxⁿ + aₙ₋₁xⁿ¯¹ + aₙ₋₂xⁿ¯² +... a₁x + a₀. If for example n = 3, then the function will be a₃x³ + a₂x² + a₁x + a₀.
Example Problem:
4x³ + 5x² + x + 6.
If let's say one coefficient is missing from the polynomial function, then the missing coefficient is defined as 0ₙxⁿ.
Lets use the same example problem only this time with one missing coefficient:
4x³ + x + 6.
This problem is missing a₂x² therefore we will insert 0x² to the function to fill the missing coefficient:
4x³ + 0x² + x + 6.
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 .
if anyone is looking for How one would factorise functions/ polynomials like the ones in the video without these factors given then use the table method
Use your calculator (go into table form) Type in your Function and where f(x) = 0 your x should tell you your solution or what to divide by
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.
The taking of class very good I can understand every thing.☺️☺️
6:36 when and what are the conditions that need to be present to use 0x²?
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.
Bruh when I was 7Th grade, I don't understand a single bit about the characteristics and components of Polynomials, but now that I am grade 10, I am understanding everything so easily, so your brain actually improves each time you age without doing anything
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
Thank you so much. Deeply Appreciated. you describe synthetic division very clearly with different examples. Please keep make videos !
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?
This video made it very easy to learn synthetic division, thanks very much. Keep up the good work.
Actually saved me from being behind for possibly the rest of the quarter. Thank you for explaining this better than my teacher ever could
Thank you sir, you are really helpful. you make things look explicit ❤
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?
You may not be my professor, but you are my teacher
Everyone : he explaied very well in 10 mins than a 2hours class in our school❤❤
Meanwhile me : watching with a lot of concentration ......
Also me : me and my last 3 braincells watching it 20mins before my final test 😂😂😂😂😂😂😂
By the way loved ur explanation ❤❤❤❤ tq so much
Found this while I'm just inches away from being annoyed with my module hahaaha. It helps a lot since I'm slow in math this has perfect explanation on how to do it it really helps a lot.
Why don't they teach this in highschool?!
I am in Junior High school rn... They teachin this... Kinda thankful..
Thank you so much. I didn't understand it the way my teacher taught it and we're testing tomorrow.
The fact that my teachers taught me using my native language but i still dont get it, but i watched this in english and i got it.
its weird
I learned 10 minutes video more than 4 hour class . Loved it thank you thank you thank you
bro comes in clutch 20 minutes before the test 😭
Thank you so much ! my professor is horrible at explaining, this video really helped me understand it !!
Me after watching OCT's vids at tests: *THIS IS BIG BRAIN TIME.*
This is a better explanation, thank you
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
You saved my life FR man THANK YOU!!
thank you, you explained better than my teacher.
Funny how I understand this in 3 mins compared to a teacher taking multiple periods to explain how to do this.
best math videos on youtube :) You're the best !!!!!
I finally understood why you have to put 0 after the number. Arghhh thankyouu you helped me so muuuch :^)
Seriously? Why though?
@@neblann It's a place holder like the 0 in 101
Thank you so much. It's really a great help. Hope I can nail our preliminary exam.
Your videos really helped me study for a test I didn't get notes on because of an absence, thank you!!
I'm here because exams are coming up, and if I get a 0 I am damn sure Imma bout to get a woopin
Philippines really said *7th Grade maths *but make it *Seniors Math*
8:00 where did you get the 0 after 7????
u the goat Organic Chemistry Tutor
Thank you i get it a little bit now
6:47 GUYS PLSS HELLP! how can I spot if I need to write that zero? is it always 0x^2 / guyzzzzzz
righttttt im so confused at that part
Guys, in the expression, since we dont have any x square, we can write it as 0xsquare
It when an x is skipped so x^4 to x^2 without x^3 probably to late tho
I learnt more Maths from this guy than I did at my school. 🤗
This is minutes before my exam and believe it or not this might just save my grade tyyyyyy if I could sub twice I literally would tyy
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.
Thanks this helped a lot!
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
Bro this shit is gold lol 95 minute class in 10:32 and so much more understandable
Today is my paper at 2:00
Bro thanks bro because of u only I can do my homework