Long Division With Polynomials - The Easy Way!

lol I had to double check my calculations but I'm glad people noticed

Thank you bro

Where did you get the 12x???

I used to do this in high school, doing it again now as an adult for fun. But I’m realizing why I was having such a hard time back then- this makes no sense.
Why in the world would I only divide and multiply by the first number? Nothing else gets multiplied by x…. Just the first number. Whether it’s x^2 in the first problem or 2x^3 in the second problem. Why????

Anybody in 2069🎉

I was confused in the last example, why did you put 0x3 between the 6x4 and (-9x2)?

45 x 3 is 135 and here my mom said weight lifting wouldn't help me in math

Anybody here in 2025?

Bro 45*3 is not 145 it is 135

Is anyone here studying a few days to exam 😅

Thank you

danko

please someone help me, will I just add 0x stuff if the following number that I will subtract on the first number is greater? is it just like borrowing?

why did you add 0x³ on the last problem? is it because 9x² is greater than 6x⁴?

In multivar watching this… is it over?

Different academic years but same problem 😞😮‍💨

Here I am, halfway through my calc 2 class, learning long division for the 2nd time.

You are my pride and joy

Anyone in 2025 !!

2025 march anyone

Thank you now i can understand much better

Thank you so much, my teacher goes through examples too fast :c

small correction at the end , 3 x 45 =135 not 145

Who’s watching in 2025

3 times 45 is 135 not 145

thank u, taught me in 5 mins

My favourite teacher 💃💃

anyone in 2025

2025 anyone??????

Anybody still watching in 2025😂

anybody watching in 1969?

You are so super smartnessssss

Thank you for the explanation

Very helpful! Thanks!

i forget how to do polynomial division every year. I'm taking integral calculus in uni right now and now im here lmao

Any one in 2040?

Bruh its 2025

anybody still watching in 2025 ?

45*3 equals 135 not 145

Years have passed yet you still haven't corrected the mistake! 3 x 45 = 135 NOT 145. From that point on the answer is wrong. Please correct it!

THANK YOI SO MUCH

Can the method of long division with polynomials be used for division in general? Short answer, yes.

Here's an example.
8547 / 231

We can treat this as (8x³ + 5x² + 4x + 7)/(2x² + 3x + 1), where x = 10.

Divide 8x³/2x² to get 4x
Multiply 4x by 2x² + 3x + 1 to get 8x³ + 12x² + 4x
Subtract 8x³ + 12x² + 4x from 8x³ + 5x² + 4x + 7 to get -7x² + 7
Divide -7x²/2x² to get -7/2 or -3.5
Multiply -3.5 by 2x² + 3x + 1 to get -7x² - 10.5x - 3.5
Subtract -7x² - 10.5x - 3.5 from -7x² + 7 to get 10.5x + 10.5
Since 10.5x + 10.5 is less than 2x² + 3x + 1 we can stop.
This means that (8x³ + 5x² + 4x + 7)/(2x² + 3x + 1) gives us (4x - 3.5) + (10.5x + 10.5)/(2x² + 3x + 1)

Now, what if we redo this, but replacing x with 10? We get the following steps:
Divide 8000/200 to get 40
Multiply 40 by 200 + 30 + 1 to get 8000 + 1200 + 40
Subtract 8000 + 1200 + 40 from 8000 + 500 + 40 + 7 to get -700 + 7
Divide -700/200 to get -7/2 or -3.5
Multiply -3.5 by 200 + 30 + 1 to get -700 - 105 - 3.5
Subtract -70 - 105 - 3.5 from -700 + 7 to get 105 + 10.5
Since 105 + 10.5 is less than 200 + 30 + 1 we can stop.
This means that (8000 + 500 + 40 + 7)/(200 + 30 + 1) gives us (40 - 3.5) + (105 + 10.5)/(200 + 30 + 1)

Now what happens if we simplify (40 - 3.5) + (105 + 10.5)/(200 + 30 + 1)?
(40 - 3.5) + (105 + 10.5)/(200 + 30 + 1) =
36.5 + 115.5/231 =
36.5 + 0.5 =
37

Therefore, 8547 / 231 = 37.

Of course, this there is by far a much quicker way to divide 8547 by 231 - you can simply subtract 231, or a multiple of 231 from 8547 until you reach 0.

8547 - 4620 = 8547 - (20 x 231) = 3927
3927 - 2310 = 3927 - (10 x 231) = 1617
1617 - 462 = 1617 - (2 x 231) = 1155
115 - 1155 = 1155 - (5 x 231) = 0

Therefore, we have a total of 8547 - (20 x 231) - (10 x 231) - (2 x 231) - (5 x 231) = 0
This can be factored as 8547 - ((20 + 10 + 2 + 5) x 231) = 0
Therefore, 8547 = (20 + 10 + 2 + 5) x 231 = 37 x 231
Therefore, 8547 / 231 = 37

45x multiplied by 3 is 135x not 145x

12 minutes ago i was a boy now i am a man 👨

This ain't gonna help me in the real world

I was so irritated from algebra but now i understand everything. Thank you very much it is a very good explanation.

Thanks a lot sir u helped me learn ti instantly i had annual exam tommorow and was worried how to solve it 😢😊thank u very much