Long division of Polynomial

追加: 2026-05-09

[00:00:03]Before we do the long division of polomials, we must know some key words.

[00:00:08]Let's take a simple example first. 7 / 3.

[00:00:16]Method one. Here are some keywords.

[00:00:20]We have the dividend, the divisor, the quotient, and the remainder.

[00:00:30]Method two, 7 / 3. 7 is not divisible by 3. Bring down the 7 to 6 + 1. 6 / 3 is divisible.

[00:00:45]We get two. 1 on the other hand is not divisible by 3. Leave it as a fraction.

[00:00:53]13 day. So the keywords remainder is one, the divisor is three and the quotient is two.

[00:01:10]Now we have a polomial of degree 3 / x + 3. We put the division symbol and we put the polomial at the right place and the divisor. We have two characters now. Mr. Polomial and Mr. Diviser.

[00:01:29]Mr. Polomial will say divide me to the Mr. Diviser.

[00:01:34]Mr. Mr. Diviser will look at all the terms of the polomial.

[00:01:41]He will pick the highest degree of x there which is 2x cubed and try to divide x + 3.

[00:01:50]Instead of getting the three involved, it will just do 2x cub / x. If you write the answer on the top day, x * what will give me 2x cub will be maybe x 2? Let me just start off with x 2.

[00:02:11]So if you put the x 2, we look x * x 2 will give me x cub. Yes. Close. But there's a missing two. So let me put a two.

[00:02:24]There we go. 2x^2 there.

[00:02:29]So Mr. divisor will tell Mr. polomial I will give you the answer 2x² it is almost close to the polomial and you know the whole polomial has uh four terms there and Mr. divisor will give additional information to Mr. polomial.

[00:02:47]The additional information will be written below the polomial.

[00:02:53]The additional information will be the product of the Mr. divisor with the answer that 2x 2 gave. So 2x 2 * x will be 2x cub plus 3 * 2x 2 will be 6 x 2 and put the answer below the polomial.

[00:03:17]This is the additional information to Mr. Polomial.

[00:03:28]Draw the line.

[00:03:38]Now the Mr. Polomial will look at the information extra information that Mr. Diviser has provided. 2xqub + 6 x² Mr. polomial will cross check with the original polomial there and see yes Mr. divisor. You did a good job. 2x cub. I wanted 2x cube. You gave me 2x cub. Well done. Well done.

[00:04:04]I wanted 5 x 2. You gave me 6 x 2. Uh I wanted 5 x 2. Not 6 x 2. You gave me an extra x 2. Take away the extra x² there.

[00:04:16]So take away. So Mr. Polomial will say take away the x². Now I do not need the extra x² there.

[00:04:27]In addition to that Mr. Polomial will tell Mr. divisor well in addition to that you might as well deal with my extra term my next term which is min - x - x there deal with this.

[00:04:44]Okay.

[00:04:46]So Mr. divisor will look at - x^2 - x ah I need to provide Mr. polomial a solution for - x^2 - x so Mr. divisor will look at the highest term there, highest power there, min - x^ 2. So x * what will give me - x^2 there? So we can guess my next answer will maybe minus x perhaps. Let's put in there first.

[00:05:23]Next answer that Mr. Diviser will provide to Mr. polomial minus x the next close answer. So we can test it now. x * - x will be - x^ 2. Yes. And 3 * - x will be - 3x. Okay. So Mr. Divisor will give the Mr. Polomial Mr. - x and extra information will be - x^ 2 the product of the d uh the product of x + 3 and - x now - x 2 3 * - x will be - 3x there so Mr. divisor will provide Mr. polomial - x as the extra answer extra information - x^ 2 - 3x you repeat the story now again Mr. Polomial we'll check now I wanted - x^ 2 Mr. divisor you provided min - x thank you minus x I wanted min - x but you gave me min - 3x there you gave me - 2x as an extra remove the 2x - 2x there so we have 2x here 2x Now Mr. Polomial will say to Mr. Diviser, I have 2x. I want you to solve it in addition to 2x there. You might as well solve the next term there plus 6 there.

[00:07:27]Mr. Diviser will look at the 2x + 6.

[00:07:32]will guess what is the next possible answer to give to Mr. Polomial.

[00:07:37]It sees the X here. Mr. Devisor is holding the X and the Mr. Polomial wants 2x there. So it'll say uh I think I can solve this. Mr. Devisor will say maybe I'll give him a plus two there as an extra answer.

[00:07:58]So let's see.

[00:08:00]Mr. divisor gives the answer to Mr. Polomial and extra + 2 2 * or x * 2 will give me 2x that's the extra information for Mr. polomial x * 2 is 2x 3 * 2 is 6 there that's extra information Mr. divisor gives to the Mr. polomial.

[00:08:38]Now it's the job of Mr. polomial to check. Well, Mr. Diviser, yes, I wanted 2x, you gave me 2x. I wanted six there, you gave me six. Well done. Everything is done. There's nothing much I need from you. It is now remains zero request now. I don't need anything from you now.

[00:08:59]So zero and let's just subtract there basically it means so now we have solved the problem Mr. divisor has given now the polomial the overall answer 2x^2 - x + 2. This is the answer. We call it the answer or you can call it the quotient is the quotient and the remainder is zero. It can be a different number but in our case here it can be other than zero but in our case it's zero here remainder is zero. So the answer which is the quotient is 2x^2 - x + 2.

[00:09:51]I hope you enjoyed this video. Have a nice day. Thank you.