Synthetic Division... How? (NancyPi)
MIT grad shows how to do synthetic division, a shortcut for long division. It's a fast way of dividing polynomials, if you're dividing one polynomial by a linear expression like x+1 or x-3. To skip ahead: 1) For how to know WHICH NUMBERS to put in the corner of the division box and the first row, skip to time 0:22. 2) For the synthetic division STEPS of carrying down coefficients, multiplying, and adding, skip to 1:12. 3) For how to WRITE the FINAL ANSWER and how to WRITE the REMAINDER (if the last number you get is not zero, there is a remainder), skip to 3:37. 4) For what to do if you have a MISSING TERM and putting a zero as its placeholder, skip to 5:04. Nancy formerly of MathBFF explains the steps.
For my video on how to do LONG DIVISION of polynomials instead, jump to: kzread.info/dash/bejne/hISMr6SCdqrFh5c.html
For my video on FACTORING to solve for the zeros of a polynomial, jump to: kzread.info/dash/bejne/jGmB0LJylMSadbA.html
Follow Nancy on Instagram: nancypi
Twitter: nancypi
SYNTHETIC DIVISION is often faster than long division for dividing polynomials, if the polynomial you're dividing by is "x plus a number" or "x minus a number". It can be used to factor a polynomial and to find the zeros or roots of a polynomial.
HOW TO DO synthetic division of polynomials:
First draw a little corner symbol. Inside the corner, write the number that makes your denominator equal to zero. If your denominator is "x+1", you would write -1 in the corner. Then write the coefficients of your top polynomial in a row, to the right of the corner symbol. Leave space for another row and draw a horizontal line beneath that. Here are the steps to repeat for synthetic division, to carry down coefficient numbers, multiply, and add:
1) Drop down the first coefficient number.
2) Multiply this number by the corner constant.
3) Write the product in the second column, second row spot.
4) Add the two numbers in the second column, and write the sum below the line in the second column.
5) Repeat those steps until you have written a number in the final column spot below the line.
6) Write your new polynomial answer using this bottom row of numbers. The first number is the leading coefficient of your polynomial and is the coefficient of an x-term that is one degree less than your original polynomial. The second number is the coefficient of the second term, etc. For example, if the numbers are 1 4 3 2, the new polynomial is 1x^2 + 4x + 3 + 2/(x+1). Notice the last number is part of the remainder, so you write that number, 2, over the original divisor (x+1) as a fraction, for the remainder term.
Sometimes there is no remainder in synthetic division examples. If the last number you get is zero, in your final division numbers, then there is no remainder. Your final answer will just have a polynomial and no fraction term added at the end. Synthetic division is a way of factoring polynomials: if there is no remainder when you finish, you have found a true factor of the original polynomial. In the example above, if the remainder had been zero instead, the original polynomial would factor into (x+1)(x^2 + 4x + 3).
Note: also watch out for a missing term in your original polynomial: if there is no x-squared term, or no x term, etc, then in order to get the right answer for synthetic division, you will need to make sure to put a zero number in your first row of coefficient numbers, as a placeholder for that missing term.
For more rational function and rational expression math examples in my algebra, algebra 2, precalculus, and college algebra mathematics videos, and for more practice problems, check out: nancypi.com
Пікірлер: 225
the problems are hard and all, but i'm more impressed about how neatly she writes backwards
@7steve777
3 жыл бұрын
fax
@nithinsabu4808
3 жыл бұрын
U seriously think she write backwards? If I am not wrong, what u see is a mirror video
Imagine having her as a teacher oh my god ❣️😊😊 explains it so well
@kaylabrown5449
4 жыл бұрын
Lion Alesso oh. I’m the quiet kid
Wow that was a very quick, but effective method and taught in a precise way. Amazing!!
@NancyPi, great explanation on how to complete synthetic division but still have not seen anyone discuss the applications of synthetic polynomial division to Computer Science (Cryptology specifically), systems engineering (Control Systems design), and so many other areas. This is the real problem with HS & some college level mathematics...it is taught devoid of application and most kids wonder..why the hell do I need to know this? Most students are not going be engineers, computer scientists, mathematicians, or physicists so why are they learning info that they will NEVER use or in many cases forget by the time it is required in typical STEM tracks in College or grad school ???? Just an old engineer and OR Analyst trying to help his HS daughter learn Pre-Calc and CALCULUS...
omg how is it that you post exactly what I need exactly when I need it???? Nancy your amazing
Nancy for cpt marvel
@d3lete473
5 жыл бұрын
Yesss
Thanks for making these videos. You really help me to get through my maths course. Writing exam next Tues. Your videos helped me more than I can articulate. God bless you and your family
My textbook be using scientific space magic terms to explain how to do stuff when really it's as simple as this. Amazing.
Thanks so much, You always do a GREAT JOB!
This was too good!! Thanks for explaining it! (I love ur channel btw!!!)
Was confused cuz I missed a day of school when this was taught but watching this made me understand it clearly. Thank you!
helped a lot, thank you!!! please keep doing videos like this.
Oh how I miss the days when math was this easy! I’m taking Differential Equations now and synthetic division just showed up again. I learned it in pre-calculus but didn’t use it a single time in Calculus 1, Calculus 2, or Calculus 3. Totally forgot how to do it, so thanks for the great explanation! Important reminder to make sure you understand as much as possible in your math classes because you never know when you’ll be expected to remember something you learned years ago.
@chocolateangel8743
2 жыл бұрын
You don't have to use SD. You can also do it using an area model/Polydoku, which I think is faster (less writing) and more conceptual. You're basically viewing division though the lens of multiplication. It works all the time, and I think you are less likely to forget it.
Wow nice throwback I should think about taking clac 2. Great video as always
Thanks for these you helped me through my first semester calculus course
Many thanks for this video and all your videos. You make math understandable 😊
You, Nancypi, explain everything batter than that advanced algebra instructor that I have. He is a bit of a smart ass. Thank you for posting your mathematical videos.
You’re so great in explaining ❤️ I love it ❤️
gah, I used to always forget how to do this. 😅 My teachers would say this was easier than the long way, but both seemed pretty tricky. The missing term thing did usually trip me up lol. Thanks for the refresher! I really like how you draw it out and explain it so it’s easy to understand. 💛
@leovolont
5 жыл бұрын
Hi Sam, Yeah, in regards to either Synthetic Polynomial division or Long Polynomial Division, the Synthetic Division is easier, but only if you remember how to do it. The Long Division is almost just like regular division, it just gets clunky because as you multiply through, you have to subtract, and to subtract, you have to change those signs, and so your work gets messy.
@thea5796
4 жыл бұрын
Good luck 👍 with school
still watching these in 2021. You are a lifesaver!!!💚💚💚
Your my real teacher for this semester !! lol love your videos and explanations
You're so great, thank you so much!
Hey Nancy, do you think in addition to this you could show how to use synthetic when the number is going to be a fraction? For example when the denominator is 3x-2? You’re videos are extremely helpful for my students! Thank you so much!
good stuff should be getting more publicity, and I'm just amazed at how she can write inverted letters, my brain would fry itself if I'd tried.
Lovely and nice way to teach and explain. very helpful
thanks so much now got a help for my exam.❤ wish to have you as a teacher.
you are marvelous. You took your time in explaining every step. I've watched the videos with other people and they speed through everything without fully explaining why they're doing what they're doing. Keep up the great work beautiful.
This video was made right on time.
Thank you, you’re an excellent instructor! -Mary
the best explanation so far
Thank you so much!!! Really helpful. I have a final tomorrow!!
Thank you so much! This was very easy to follow
Can you please make a video on rational integrals that have irreducible denominators using partial fractions?! Thanks Nancy!!
is she writing everything backwards
@shashwat4920
3 жыл бұрын
A software for that is available..
@kelvin4941
3 жыл бұрын
she actually is writing it all backwards
@carultch
Жыл бұрын
@@shashwat4920 You can also use hardware to do it. Put a 45 degree mirror in front of the camera lens, and aim the camera at a 90 degree angle.
@notblizzardx
Жыл бұрын
No js inverted
Thank you Nancy!
Reminds me of horners method...might be a nice video topic :) Still pleasantly surprised to see your activity!
this girl is the only person who can teach me math
Love your lessons! Thank you....
SO easy to understand. Thanks!!!
This video is gold thank you 😍😍
Madam today I watched your video on synthetic division of quadratic equations. it is realy very. Interesting.I feel extremely satisfied tu watch your videos on maths. thanks s lot madam.Realy u are one in lakhs tu teach mathematics so brilliantly.Hats off u madam
Nancy, you are a BRILLIANT TEACHER! 😅👍🙏
Never newed math could be this eazy thanks nancy
This really helped me so much.
thank god u reuploaded this!!!
I love your way of teaching❤
You are a life saver!
Thank you! I ask all my students to view your videos.
hi Nancy thanks a lot for helping me in the past semester may you please again help me on Laplace and inverse transformations, unit-step functions and Ordinary Differential equations thank you.
i finished my math homework for the night but oh my god she’s just so relaxing
Thanks again!
Thank you so much you Nancy are super savior
Thank you! Why are math teachers and textbooks unable to communicate clearly? You are a life saver
Thank you for all you efforts, but I was wondering what is the basic mathematical formulas of all your videos
Great tutorial, any chance you would do one covering Fourier series please
This is so much fun, really enjoying your vids during my calculus class, thank you!
Everyone is saying this is calculus......i'm doing this in algebra 2....plz save me i'm dying
@Outfled
5 жыл бұрын
Mck Harris i’m watching this and i’m in algebra 1 lol
@aaliyahfeacher5427
5 жыл бұрын
Exactly I'm in algebra 2 but I'm pretty sure we'll need this for calculus next yr
@Infin3onTunes
5 жыл бұрын
same bro same.
@internetcicocuk01
5 жыл бұрын
We are doing this stuff in Algebra 2
@roboltamy
5 жыл бұрын
This isn't calculus last I checked xp
"I will come back, you were a great help" - Andrew
Thank you ma'am Nancypi
This is polynomial made easy.Much love from Nigeria
Thank you!
Thank You!
You are really the very best.
THANK YOU
Thank you queen
Excellent teaching ❤️
Tysm 😘
This explains me well.
Thank you ♡
Short and sweet synthetic division for late evening learning. Hmmm up next could be real sleep. Thank you for a wonderful synthetic night cap Nancy!
Thanks!
your great, thank you so much 🤘
thank you very much
Thank you
Her “good luck” at the end had me dead 💀
Wow, thanks!
This is so much easier than what my teacher is teaching
Synthetic Division or Long Division? For Synthetic Division -> Divisor must be in the form "x - c"; where c must be a constant
Please don’t vanish again from KZread i really missed you.. and your previous channel videos really helped me in my exams and become a reason that I scored 97/100 in my finals..
can you do a video explaining IVT and EVT???
you are good teacher thank u
The remainder 4 is actually the result of applying 2 to the polynomial like f(2). This is how clever coders apply a value to polynomials without using any power arithmetic.
Can you do stuff on 3d vectors? Parametric equations and what not?
i hope you come back and make more video
brilliant...
She's back?!!😃😃
thx for the help :)
Mam please make a video on the derivation of synthetic division
Liked,subbed,saved.🤠Thank you.
Please make a video on conic section
How does she write backwards like that? From her point of view she should have to write backwards so we can see it forwards...
@ev25zv
4 жыл бұрын
She's an MIT grad... or she's just right-handed and flipped the video image in post to make the writing forward.
Wow u teach us very nice
U are making mathematics look easy
please make video for First Order Differentrial Equation. There are 5 types which are; seperable variable, linear, exact equation, homogenous and Bernoulli equation. I hope you read my comment & Im enjoy your video bcs I understand. Love from Malaysia ❤
Love you teacher
Omg thank you!! You teach better than my professor
Hey Nancy, I would like to make a content suggestion over here, not because i think I'm any smarter than you or something.....but because i feel that your videos don't really communicate the beauty and joy of solving maths. in that part i will like you to provide more reasons as to why we solve things the way we do and provide context to why each step is carried out. i understand that the proofs for some things might be too complex but there are simple proofs out there as well that are lesser known to people, i think that your channel can provide people with these proofs so that they are able to appreciate the simplicity of maths and not be afraid of it. also why do we need solutions, what do solutions mean and whats the importance of making any mathematical simplification or step. these are question that when answered leave a deep level of clarity about something in peoples mind! atleast thats how it worked for me! i used to run from maths!
@leovolont
5 жыл бұрын
Hi Abdul, Well, a lot of these kids are being rushed through the system. there heads are spinning. They are so hurried that they don't take the time to step back to even see what they are really doing. But us old men can relax and take our time and see how cool this stuff is.
@skylerhill2945
3 жыл бұрын
Nobody will ever use this bullshit other than to get their degree. There is no beauty or joy in the math. Shes the beauty and the joy.
For the placeholder thing,why would it be there if you put it into standard form
Tank you!
this is sooo awesome love your videos ma'am love from india