How to do Long Division with Polynomials (NancyPi)

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.

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.

[matiasbeccaglia]

She taught me in 15 mins what whole week of class couldn’t

[treeobservation]

You have no idea how easy it is to listen to a person speaking clear english. Thanks again

[mikekeenan]

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

[chrisp]

Currently in Calculus 2 and coming back to this for integration by partial fraction decomposition. Super helpful!

[mrjayd]

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

[gammadelray]

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.

[MyWhyU]

Nancy: Your explanations are beautifully done and a real inspiration. Thank you and keep up the great work! - Steve Goldman of Why U.
P.S. I love your "reverse" writing trick. I assume that you are actually right-handed! :-)

[geetikaadhikari]

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

[javierarguelles]

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

[jodileben]

Thank you so much! I didn't do well at math in school and nearly 30 years later I'm going back to college. Math brings me instant anxiety simply because of feeling like I don't understand. Your explanation was very helpful!

[mialeonard]

I really like how you explain the steps of each different problem, because I like to skip ahead to the type of problem I actually need help with.

[ogmarksu]

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

[estebanzd]

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.

[hellokitty-lwmb]

This is the most helpful video on polynomial division on youtube. Thanks a ton Nancy!

[negativeM]

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.

[shylingg]

0:16 "And now it's come back to haunt you in highschool"
Me, in junior high: :')

[TheSudouser]

I frequently come back to your examples as a refresher. I was reviewing eigenvalue/eigenvector problems and polynomial division was required to obtain the eigenvalues and this once again helped me remember. Thankyou Nancy!

[IvanMTG]

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

[brookestephen]

i'm still mesmerized when you write backwards so well! Thanks for making these subjects understandable.

[adoreve]

Vine por Aidan 😳✌️❤️
Igual gracias por la explicación JSJSJ🍋✨