MIT grad explains how to do long division with polynomials. Here I show clear steps to divide two polynomials using long division. I give two examples, one basic example as an introduction to the steps, and one more advanced example. Nancy formerly of MathBFF explains the steps.

Follow me on Instagram! https://instagram.com/mathnancy

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The steps for long division of polynomials are the same as for long division of numbers and can be summarized as:

1) Find how many times the first term of your divisor (on the left) goes into the first term of your dividend (on the right).

2) Write that number (or "x" expression) on the top line above your dividend, aligned vertically with the term it's most similar to (like term).

3) Multiply that number (or "x" expression) by each term in your divisor (on the left) and write that result on the line directly below your dividend.

4) Subtract the second line from the first line and write your result below.

5) Drop down another term from your dividend into your bottom line.

6) Find how many times the first term of your divisor goes into the first term of your bottom line and write that result on your top line above the dividend, aligned vertically with the term like it.

7) Repeat steps #3-6 until the first term of your divisor cannot go into the first term of your bottom line result anymore. This bottom line expression is your remainder.

8) Your answer is your top line result plus your remainder over the divisor.

For more of my math videos, check out: http://nancypi.com

I’m glad you’re back! Wish you the best with this new channel 😃

which is that old channel she is representing before

Hello

Never been so early 😂

Miss you Nancy 😩😍

Maybe use addative primary colors or florescent colors to increase the contrast?

so unnecessary 😛

Two vids in one day? Nice! Hope all is well Nancy!

Nice video Nancy!

I 💜 you Nancy .

I love😍😍 uuuh🙊

WE MISSED YOU!!

Awesome.

You can also use synthetic division when dividing a polynomial by a binomial instead of long division.

Metal Mandalorian I actually find synthetic one quite funny 🙂 though i only use long division

for synt. division the divisor must be a linear binomial (exponent of 1). So for the first problem Yes

Good work Nancy

Thanks for this, I find this very difficult!

Ahmed, there is no such thing as use full you should say useful.

Dank Memes but it came from use +full so it become useful

Ahmed Mzhr You are illiterate

Dank Memes lol I’m illiterate but who think about Grammer and vocabulary lol for you

Ahmed Mzhr I’m sorry I can not understand you please speak proper English.

NANCY…. Did you narrate and produce videos for a coursera project? Voice sounds very similar

Thanks for teaching me long division of polynomials .

Thank you

Nancy! I’m glad you came back!

And thanks for the video, it really helped me with this, I’m currently viewing this in school and it was a pain.

I wish my teachers had told us to use parentheses for the subtracting part like you did. Would have prevented a lot of errors.

I’m surprised they didn’t because if they didn’t use parentheses the way they taught you is wrong

@WHEELZZ Sums up my school years in maths,

I have a division problem Madam. How to divide 1-a^2-8x^3 -6ax by 1-a-2x

Can you please go over matrices.

yes 💕

How to use long division.. *”every one’s favourite”*

TF?!

tfw sarcasm

Thank you Nancy for your videos they help me a lot and i hope you keep going to make more i really appreciate that

gib clay

In the 1st question the remainder is wrong it should be -3.

No it shouldn’t

You kind look like my Math Teacher, i hate her, but i don’t hate you, everyone in class hates her she doesn’t even know how to explain well…i got 4/20 last quiz and it pisses me off, cause she blamed me for not listening to her in class, i was listening but she was just talking gibberish, i like how you explained it, it really helped me gain higher grades😢😢😢

thank you so much

It’s easy

you look tired Nancy 🙁

Im not listening to my teacher in math I understand this better

Anyone else noticed that she uploaded a mirror version of the real video. That way everything would not be flipped around since she is writing on a glass.

lol my teacher don’t know it a high school teacher and there was an example of drawing function using derivatives and i was confused until I see your vid

What if the constants are not divisible?

Thank you soooo much!!!!!!!

taha

how is she writing backward like that????

I’m also thinking that’s ??

she wrote on the fiber glass 😂😂😂

@Ian Siegel Nah, she is an actual genius that can write backwards

That’s actually a skill that was used on WW2 aircraft carriers.

@Derek no no no! See, he had evil parents who though they were funny and only taught her to write backwards! Now she is incapable of writing forwards and this is her only career option!

Miss Nancy ,u look upset during this video.Be Blessed

Is she writing backwards?

Very Helpful

I will do my best to get better in polynomial division

how to take lcm in partial fraction

thanks!

i was really struggling with this but your video and the steps in the description made it really simple!

Thank youuuu

Thankn you TT

first go and lrn how to divide polynomials .[(x+1)(x+2)]+3 is right

The divisor got me but now I know there’s a 0x.

Super helpful!

This helped a ton

cant thank you enough

Nancy, you’re going to help me pass an engineering exam! It’s amazing how this elementary division has came back to haunt, lol.

Oh god, I have to revisit this in college?? yay..

Hi Nancy

I am on the East Coast and I do love pasta. East Coast of Australia that is, if you come to Australia say Hi.

Pacing of you videos is perfect, enough time to put my own answer if i have it but not so slow that I am waiting if I don’t. Voice is not harsh or gating like some presenters.

I have returned to learning at 55yo. Eng degree so maths is important. You and SnugglyHappyMathTime have been a great help.

Tanks

Advance algebra

Why do you have to add the 0x to one but not the other?

Thank you so much. Brilliant

Nancy, I really love your videos. You help me so much. High school for me was 2000-2004 so it’s been a while. Now I’m in the university and we are doing these types of problems

Thanks for the clarification Nanci! Studying for my CLEP exam and this was helpful.

Thank you so much! I have a test today and this was extremely helpful!

Thank you so much i understand it now. I like how you explain why things are done, it is easy to follow you. You have helped me with all my exams. Thank you.

Got that right

“Came back to haunt you in highschool”

And in College

is she okay?

She doesn’t look well..Like she is depressed or something

Hugh Jass yeah she’s probs tired of lookin at ur dumbass comments

Bunnylow hehe

wow what an insult how old are you 12

you make thinks look so easy! Thank You!

didn’t get any of that smh

Excellent step by step explanation Nancy! I like your teaching method. And I enjoyed watching how you taught the integration by parts and u-substitution techniques.

Ugh god bless you! You’ve helped me understand if I hope I pass my math test tomorrow

Great, thank you. But the problem I’m having is a bit different. There are functions in Matlab (and Octave) called “lqe” or “lqr”, solving ;linear quadratic systems (Riccati equations ?) I’m trying to find an explanation of how those functions work. If those are somethings you can explain I would love to see it.

Nancy, you should start a Tutoring service to boost that income a little more, and help us struggling students!

Hey Nancy can you teach me integrals

love ya ❤️

I love you, thank you.

No thanks

The funny thing is the way she talks and her mannerisms remind me of my actual math teacher.

Nice vedio

Nancy you are the best YouTube teacher 👩🏫😍 ever

Ty

big thank u , i’ve been struggling doing this since high school , but now i’m a master

thankuuuu

Just a recommandation for when you have a place holder for X. 1. you can not put anything there since many people should not need one. If you have to right now you need to put a 1 as a place holder so 1 times X = X but right now you are saying 0 times X = 0. Just a thought! Thanks! Like the Video!!!!

3x minus x = 2x so no 3x minus 0x = should be 2x but you have it as 3x?????????????????

Very well explained, you have helped me overcome my fear of this very complicated process.

👏👏👏

-0x square + 10xsquare = 9xsquare

Brilliant

선생님은 감사합니다

BLACKPINK😂😂❤️

I have a problem where my second term and and my multiplied second term have different degrees. What would I do then?

Yeahh i really understood 😊

Thankyou. This video is very helpful.

Thanks. It really did help

what is with youtube and these shit ads, ofcource i hate studing and i hate math the hell are you reminding me of that for, why do u think i youtube this video. get the f out of the way.

Another tip is to simplify the polynomial first to save time. For the polynomial you can write (x^2+x+2x+5)/x+1, then split it into two fractions into (x^2+x)/x+1…this simplifies to x+ (2x+5)/x+1

I am in love with you 😍

I really need thiss

very nice

Really great video, I’m in eighth grade and this video really helped me understand what I didn’t get in class. Thank you so much!

she just solved my problem…..thank you

Thanks ma’m

I have an engineering degree and never learned this til now.

Thanks.

hans how did u graduate without knowing this?

Thank You 😊

You lost me at, “polynomials”

Did she stop recording videos? I haven’t seen any new video of hers

Partial fraction decomposition is another useful algebraic skill in higher math that may not come easy at first.

You look tired babe, have some rest. Thanks for the lesson btw, i understood everything you were talking about.

i thought the same

Thanks Nancy This really helped when u said put the distributed part under the polynomisl And to line them up (:

I prefer the Reverse Tabular/”Box” Method for solving such problems because into the various Area Models when doing multiplication and division. I think it’s an easier algorithm to commit to memory, and it allows you to see how the numbers come together.

Is the 0x really necessary? Sure it might be more formal but surely it doesn’t affect the solution or the steps at all.

when working with large gaps between polynomial terms e.g x^5 and x^2 , it helps keep it more ordered so you can write your next steps in the right spot

Thanks so much..

You saved me..

I love dis appreciate,,,

Plz do roots of quadratic equations… Thanks

X-1/x+1 how

how do you write so quickly backwards that’s amazing ?!?!?!??!?!?!

she writes normally then inverts the video. It is backwards in real life, but because she flips the visuals it is normal post edit

I can’t believe I understand

Taking cal 2 this semester and these came up and I completely forgot how. This was a perfect refresher!

I always get super excited when I look up a concept and one of your videos pops up. Because I know afterwards I will actually understand it better.

my algebra teacher is normally very good but man he confused me on this badly. this video clairfied me on this. Thank you!

Are you really sad and upset or that’s just your normal facial expression?!

Good makeup

OMG! ty, bring me hither thine face that I might kiss you- MWAH!

3x times 0x is 0 not 0x^2 wtf bruh

Yosef yes it is

Thank you so much Nancy! This is no longer my nightmare 😀

👍🏼🤪

mann, it is crazy how i’m so entertained by this teacher. she speaks english and she is teaching me something

11:07 this made me laugh😂

Math makes me want to cry

You and me both;;

It’s not my level of knowledge, it’s about that:

At least ya wont cry alone.

Why 😏

Only when you don’t get anythig and you test is tomorrow

thankyou!

Math is always fun with Nancy.

I learned this in 9th or 10th class

But today I have bio..and a dream to be a doctor…but still physics contains many calculation😅

Thanku so much…this was really helpful!!!

you probably hear this alot but you look like an A.I🤔🤨

Thanks for the help had an upcoming test and I didn’t understand how to do the long division part until now thanks! 😀

Nancy is Better than my teacher at school!!!!

Can you please explain the algbaric identities.

I searched for help on this topic, this didn’t come up until I clicked in and when I seen it I went here instead

this was really helpful, thank you, I’ve got my OCR FSMQ paper tomorrow (now that i have finished my actual GCSEs) so this will come in handy, Cheers!

Thank you very much Nancy! This will help me a lot tomorrow with my regents.

I love that you can make this easy for people to understand BUT when do we really need to use this in our daily lives?

People really ought to question why they need to learn this. I’ve learned this in high school. And I have NEVER EVER needed for anything in my daily life. It’s a redundant topic in math that the system makes kids learn for nothing.

Instead of teaching kids to manage their money, how to invest, diversify, they teach this junk… no offence to what you’re doing.

But really? Why bother to learn this stuff when you’re never going to need it.

thank u NANCY I was not understanding this

Any one from India

🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳

Isn’t anyone going to notice how she wrote it TOWARDS us…

Thank you mam

No Sleep Nancy….

Pls do rates of change

thanks

Wow …..nancy said that was fun..! God bless your heart

Hey Nancy thank you. You are smart enough to make this soo easy for me, you related to Inanna? She is a goddess also. AKA Ishtar, Venus, blah blah blah . I bet you’re right handed too

Who want to go to mars!

who writes that way

she is writing each word the opposite side

Honestly thank you so much. This is the first video on this I can honestly understand

thanks learned alot

your the best teacher

How do you know where to put the 0x term?

Easy. Thank you

Thanks a lot. That’s a very important subject.

3x times 0x is just zero.

Is she writing in back words

I slept in my class because I knew that your video would help me understand the concept better and i was right. 😄😄😄😄 Thank you Nancy!

Nancy, could you also show how to solve long polynomial equations? With another equation on the other side of the equals sign.

NANCY! THANK U SM <3333 if you have the expertise, can you make organic chemistry tutorials and physics videos as well? those would be really popular, as the only good chem tutor on YouTube is Melissa Maribel! Thanks!

Thanks! My teacher was far less clear describing this. he just told us to add a zero whenever it makes it work but never told us why or how!!

Does she write all of this backwards? That looks complicated

LittleGreenFriend i was about to ask that very thinf

U are so beautiful

Tahira Madri i bet one thousand dollars you are indian

I love you

Nancy you are a very good math teacher. Thank you.

“I got it made! I’m hot for teacher.”

Nancy, You have cleared up my confusion!! Thanks a lot 😊!

Thnk youuuuuuuuu so much i understand it better now💓

0:16 “And now it’s come back to haunt you in highschool”

Me, in junior high: :’)

It’ll come back in college as well

thank you!

You explained this very well, which is good or else I would have failed lmao

الي خاش يكحل ب المزه لايك

The trouble is with “new math”/”common core math” they don’t learn long division. Drives me insane!

Hi madom iam from India…. super teacher….I can understand easily this method

Thanks! It really helps alot

she looks stressed… like me LOL

It may be, because she looks into inverted numbers on a glass (mirror way)

Minmin Chan yes ..shes looking in stress

Who your mother is stresed. You fool

Lol I can barely see anything that’s over your face 😂😂 great video

Is it me or its more understandable if you listen math on youtube more than at your teacher in school ^^

Thank you so much for this video. It helped me so much.

thanks for that, loved your way of explaining

Wow, I the best Maths teacher in YouTube

also check out the Organic Chemistry Tutor. He does maths and science and is very good.

Thank u save my Grades!!!!

God bless You!!!!🙏🙏😥🙏🙏😫

I thought 3X*0X would just equal 0, not 0x^2.

P.S please correct me if I’m wrong, my math is very bad.

You cannot multiply the 3 by the X, only the X by the other X. In 3X*0X, 3*0=0, but X*X=X^2. That is why 3X*0X= 0X^2. No worries, you will be an expert in math one day!

thanks

کوڕە بژی ئەرێوەڵا ❤

Thank you so much for it

thank you .

We always called this Synthetic Division.

ThankU sooo muchhh!!

Lifesaver!!!♥️

Hi Where do you live di.

thx you Nancy!

How did she know im in high school

Where is this used

hay NancyPi How can I do this operation: 1/p(x) ?

NancyPI WHO TAUGHT you this black magic and is it necessary

I see u Miss looking kinda cute ahahaha

very nice !

Thank u its make me understand easier

I still don’t understand why we need a place holder of 0x.. never mind I get it

thank you very much

Nancy: You are fantastic, amazing, clever!! Love your lessons!! Kisses. Pedro

How about we just have all these youtubers be teachers then we can all not be stupid.

I don’t seem to understand the answer on the last expression…. can you explain it?

Thanks very much for the video nancy sis

Helped me a lot

I understand you more than my actual teacher thank you so much

Mas naintindihan kopa tong english na turo kaysa sa turo ng teacher ko na filipino

Nancy, Can You Do My Homework?

Hey Nancy! Could you please do an Integration by Partial Fraction Decomposition video??

Whoever made math, why didn’t they just stop at the basics? 😂

Because the more advanced maths have more applications, and they’re all necessary. I know it’s complicated, but don’t give up.

helpful video! ur kinda emotionless, it startled me for a second LOL

Math is really a sad story that makes me cry 😂😂

baby i was share you

Omg this helped me,thank you very much

I like your teaching way better than my algebra teacher @Nancypi #Nancypi

THANK YOU

Thank you 😭

nancy you better take care of yourself

Thank you so much NancyPi this video was very helpful. I officially LOVE long division.

*What? Still searching YouTube for math hel—*

Very nicely explauned Thank you!…

Thank u

Thanks you 🙏🏽 and…FOR THE REPUBLIC

excellent

from India

I’m just impressed she’s writing backwards

Extremely Helpful!

daaam, this helped me soo much.

Thank you for your time and energy

It’s easy for me now tq

VERY HELPFUL

Nancy is the best!

Thanks for explaining this!!! Makes a ton more sense!!!

I’ve never been good at Regular Long division, this is going to kill me

Uhh… thanks Nancy. I never learned this in school. Needed it to solve an integral just now. Yay uni I guess…

Nancy, I wanted to share this thought with you. I would to see you start at a beginner level and you would know the progression to move to the next video. It would be like you having 2 channels. You are good at what you do.

Crushed

+rep

stop writing on my screen

Thanks Nancy. It was so uncomfortable

Props for being able to write all of that backwards! Thanks for sharing 🙂

You are a good teacher

I just realised you are writing in reverse, damn, thats a cool skill!

when her reverse hand writing is better than your normal hand writing

Yep I did not understand long division in primary, and now it suddenly returns to haunt me in Matric.

I wish you were my teacher

I actually love math but it’s been 10 years since college and now I’m going back for another degree and I can’t remember anything with math. This breaks it down so I can just jump right back on the horse. Thank you for the clarity in your explanation.

WOW! You are really a Smart Teacher

Your method of teaching is as good as you are…

…u know noam?

mam nice explanation.

Do we need to understand why we do these steps or just how to do them?

Is she writing all this backwards or is it just me?

save her. period. send.

long division always comes back to haunt u => 10:15 most students

Great job Nancy. Your patience is like a person from Seventh-day Adventist background per Revelation 14:12. God’s blessings. Thumbs up if you agree 👍

Thank you Nancy really helped for my upcoming test ur awesome 👍

Thank u

This is great stuff to learn from. I’m even learning a lot from Nancy’s channel know how good I am at math and calculus. Never did I know this until I found this video. Or I probably learned it in the past but its been so long. Its always good to get the review in.

most people can’t write backwards, that was my interview test as a Drafter … once I realized what he was making me do by not letting me turn the paper around I about busted a gut

I was completely blank in this concept and I wanna learn it….and u were the only one to help me out of this stuff…really thanks to u

This beautiful young lady has the ability to turn a mammoth task into a cinch.

Very good instructions.

Thanks

Thank you so much, I understood this concept really well

plss upload more

Thank you! I finally understand this after watching over 15 videos 🙏!

I love when a good looking lady teach me math I just listen automatically lmao

im in the 6th grade… i think i came to the wrong place

Thankyou so much! your an angel in disguise. <3

hello guys,she is writing it mirrored for us,appreciate it by liking this comment

I keep forgetting this!

How u writing 🤔🤔😱😕

Wow

It really bothers me, the fact she must be writing this inverted so it looks normal in the camera…

wow you really helped me understand! thank you so much!!

thank you mam

Lol I’m doing engineering and I never thought I’d ever need this again

I like this because you teach slowly, Thanks