In this expression, we’re

dividing this third degree polynomial by this

first degree polynomial. And we could simplify

this by using traditional algebraic

long division. But what we’re going

to cover in this video is a slightly

different technique, and we call it

synthetic division. And synthetic division

is going to seem like a little bit of voodoo

in the context of this video. In the next few

videos we’re going to think about why it actually

makes sense, why you actually get the same result as

traditional algebraic long division. My personal tastes are not

to like synthetic division because it is very,

very, very algorithmic. I prefer to do traditional

algebraic long division. But I think you’ll see that

this has some advantages. It can be faster. And it also uses a lot

less space on your paper. So let’s actually perform

this synthetic division. Let’s actually simplify

this expression. Before we start, there’s

two important things to keep in mind. We’re doing, kind of,

the most basic form of synthetic division. And to do this most basic

algorithm, this most basic process, you have

to look for two things in this

bottom expression. The first is that it has to

be a polynomial of degree 1. So you have just an x here. You don’t have an x

squared, an x to the third, an x to the fourth or

anything like that. The other thing is, is that

the coefficient here is a 1. There are ways to do it if

the coefficient was different, but then our synthetic

division, we’ll have to add a little bit of

bells and whistles to it. So in general, what

I’m going to show you now will work if

you have something of the form x plus or

minus something else. So with that said,

let’s actually perform the synthetic division. So the first thing

I’m going to do is write all the coefficients

for this polynomial that’s in the numerator. So let’s write all of them. So we have a 3. We have a 4, that’s

a positive 4. We have a negative 2. And a negative 1. And you’ll see different people

draw different types of signs here depending on how they’re

doing synthetic division. But this is the

most traditional. And you want to leave

some space right here for another row of numbers. So that’s why I’ve gone

all the way down here. And then we look

at the denominator. And in particular, we’re

going to look whatever x plus or minus is,

right over here. So we’ll look at, right over

here, we have a positive 4. Instead of writing a positive 4,

we write the negative of that. So we write the negative,

which would be negative 4. And now we are

all set up, and we are ready to perform

our synthetic division. And it’s going to

seem like voodoo. In future videos, we’ll

explain why this works. So first, this first

coefficient, we literally just bring it straight down. And so you put the 3 there. Then you multiply what you

have here times the negative 4. So you multiply it

times the negative 4. 3 times negative

4 is negative 12. Then you add the 4

to the negative 12. 4 plus negative

12 is negative 8. Then you multiply negative

8 times the negative 4. I think you see the pattern. Negative 8 times negative

4 is positive 32. Now we add negative

2 plus positive 32. That gives us positive 30. Then you multiply the positive

30 times the negative 4. And that gives you negative 120. And then you add the negative

1 plus the negative 120. And you end up with

a negative 121. Now the last thing

you do is say, well, I have one term here. And in this plain,

vanilla, simple version of synthetic division, we’re

only dealing, actually, when you have x plus

or minus something. So you’re only going

to have one term there. So you separate out one term

from the right, just like that. And we essentially

have our answer, even though it

seems like voodoo. So to simplify this, you get,

and you could have a drum roll right over here,

this right over here, it’s going to be

a constant term. You could think of it

as a degree 0 term. This is going to be an x term. And this is going to

be an x squared term. You can kind of just

build up from here, saying this first one is

going to be a constant. Then this is going to be an

x term, then an x squared. If we had more you’d have

an x to the third, an x to the fourth, so

on and so forth. So this is going to be equal

to 3x squared minus 8x plus 30. And this right over

here you can view as the remainder, so minus

121 over the x plus 4. This didn’t divide perfectly. So over the x plus 4. Another way you could have

done it, you could have said, this is the remainder. So I’m going to have a

negative 121 over x plus 4. And this is going to be plus

30 minus 8x plus 3x squared. So hopefully that

makes some sense. I’ll do another example

in the next video. And then we’ll think about

why this actually works.

What sorcery is this?

aka polynomial division. you just need to understand fractions.

LOL I can't stop laughing, that's exactly what I thought.

I found my son watching this video and when I got to him his brains was scattered all over his desk. Now im on the run from the cops. Dont let your kids watch this by themselves you will be sorry!

Oh honey… I'm in 12th grade… it'll be back to get you when you least expect it

Interesting technique. Seemingly synthetic division is traditional division that has been "flipped" around. Everything(even the division bar itself) is turned around. Multiplication is performed by the opposite of the denominator and instead of subtraction, addition is used in the synthetic version and the corresponding variables are assigned to the results, making the calculations faster and not as messy as the traditional method.

i dont understand the whole move one to the right

does he have a video of the extra bells and whistles required to do this when the coefficient of your divisor isn't 1?

Something I'm already better than you at π

Yay, cookies are way better than synthetic division.

that is what i think when i listen to my teacher

this is so much easier than long division with polynomials

Oh Asians.

Math? Never heard of it.

Holy shit, Mind Blown.

That's not algebra, that's voodoo magic.

Are you a wizard?

Thanks for sharing…

Hahaa sure is π

You must be Asian. And I must be racist…

Nice.

1:58 lmao

My mind just got fucking blown.

thumbs up if your in seventh grade.

middle schoolers up in here sayin they're doin this, meanwhile I'm in college having to do this DX

Cool

11th grader π³…. I feel dumb

tooo long

Thanks! I'm in 9th and I'm in algebra 2 honors, and my teacher doesn't describe the lesson well this helps a lot!

subscribeyou make it easyer to understand! Precal and algebra 1 for collage here i come! (Nxt year) ;-; ~tearHe makes me laugh sometimes "it may seem like voooodoooo" π

I appreciate this guy for making these vids, but I can't stand the way he talks… he comes off as a tool…

you da man thanks

Nvm I understand but what do you do when the x isn't an x. Say its 9x

Amazing video; thank you very much

thank youππΌ

This is sorcery

Wasn't paying attention in class today so I missed this lesson in class… Thanks!

Dude. You're a freaking legend. Your help is much appreciated. Keep it up!

when exams are coming up and u need to be refreshed

Hey, I don't understand you said there would be square 3 but where is the x coming from?, should I just follow that without any reason? please help.

VOODOO MAGIC

Dude! what method are you using?

I find this video offensive I'm an active voodoo conjurer.

Extremely helpful, thanks a bunch

do synthetic division with numerical coeficient

do it if its no voodo magic!!!

#dooksrR'us

10 questions 1. Are you sure you cant do it with coefficient? do you know binary?

Thanks for the tutorial, you explained it better than my teacher did. It really is voodoo!

what happens if your remainder is zero

today is my exam lol thbx

I love learning math at home because i can say "Oh shitttttt" and "HELL YEAHHH" whenever i get something.

Why do you put the opposite sign. Like if it's -2 why do you put 2? Thanks! π

Thank you

Dude thanks! you helped.

I've always heard, "Set (x + 4) = 0" But same concept, same result using the negative of 4 ( -4 )

Sal Khan is the math god in human form.

don't give more if one hundred twenty explanation

You are math jesus

MAGIC?

I prefer traditional long division but I had a problem that it didn't work for. Please tell me if i am making simple mistakes or synthetic only works for this problem. PROBLEM: (xβ΄β3xΒ³+x-4)(x+1)

pure magic

for the bottom equation, the one that your dividing by all your doing is finding the zero of it/roots so basically X+4 is X+4=0, that's why it is -4 and if you graph y=x+4 the root aka x-int is -4 same if you divide the polynomial by x^2-1, you find the zeros which are 1 and -1 and use it for the synthetic division(same place the -4 was put in the videos example)

Question.. why do you change the +4 on the bottom to a negative in dividing?

Thank you very much πππ

F R I K I N V O O D O O

IT IS VOOOOOODOOOOOO!!

Thank you sooo much.It help alot

Ah, thanks so much! Kahn Academy is awesome!

This video is very helpful especially for me because we are just in 8th grade but we are already studying about thism

You have saved my life!

first

So the last term is always the remainder?

i love ur language…cool

I hope that this video is more helpful then the other video.

I am so stress about our test tomorrow because i don't know how to do it.

why 3x squared? isn't supposed to be 3x cube?

At the start what if it's already negative do we change it into positive

Thank you

WOOWW BUT THE NEGATIVE IS CONFUSING ME

My class is for 40 minutes. I do not understand a thing my teacher is saying but you taught it to me in 6 minutes. Thank you

yow! thanks so much it will soon help in my ft tomorrow because i got zero on my 2 ft hopefully it will develop my score

taking my exams later and still watching this tho! much needed!!!

Starts at 1:39

Who watched this video bcuz u have Quiz for Calculas tomorrow

I just love how I can learn in five minutes what takes a normal teacher 30 minutes to teach thanks

thank you very much very helpful!

I have an exam tomorrow and finals next week :β) IM DOOMED JVKCK K K

But why is the 4 negative?

FINALLY I UNDERSTAND HOW THIS WORKS!

Im an 8th grader and we are doing this in Pre Ap Algebra 1 i didnt get it when my teacher explained it so so but this helped a lot thanks

This has saved me from having the most miserable night of precalc in my life. Many thanks!

What happens if the bottom is 2x +8?

HAVING THE BOARD BLACK AND THE WRITING SO MINUTE MAKES IT A BIT AWKWARD…DON'T YOU THINK SO!???

Really nice….sir

I have one question sal at 2:28 is there a reason why u have to take the negative?

Buuuut how about dividing with polynomials of degree greater than 1?

Every vid only shows for deg (g)= 1….:|

-1 -(-120) = -1 + 120 = -119

lol people need to stop bragging about what age they're learning this at

Thank u so much….i have an exam today..

ooooooooooooooooooooooooooooooooooooooooooooh lit

All my math teachers got confused when I used synthetic division. I just felt the "traditional" way took up way too much space.