Thanks for the refresher. I was doing nth order differential equations and needed to remember how to do this since I haven't done it in ages. Life saver, man! Thanks

@fwogboy

7 жыл бұрын

Collin Smith Same!! If only I could remember every little math lesson I've learned...

@jwloohou2

2 жыл бұрын

5 years later and I'm watching this for the exact same reason.

You're about 2000 times better at teaching this than my actual teacher is. THANK YOU SO MUCH

oh my god, i didn't know that using synthetic division could solve so much!!! I didn't even think of just keep going down further till it hit the quadratic formula!!!!! THANK YOU!!!!

Very Good! When solve fourth-order equation of one variable 2x^4+5x^3-5x^2-20x-12=0,the solution can continue appling synthetic division,for example -1| +2 + 5 - 5 - 20 -12 | - 2 - 3 + 8 +12 +2|+2 + 3 - 8 - 12 +0 | + 4+14+12 -2|+2 + 7 + 6 +0 | - 4 - 6 |+2 + 3 +0 So follow factorization,original equation can be changed into (x+1)(x-2)(x+2)(2x+3)=0 好棒! 当求解一个变量2x ^ 4 + 5x ^ 3-5x ^ 2-20x-12 = 0的四阶方程时，其可以连续应用综合除法，例如 -1| +2 + 5 - 5 - 20 -12 | - 2 - 3 + 8 +12 +2|+2 + 3 - 8 - 12 +0 | + 4+14+12 -2|+2 + 7 + 6 +0 | - 4 - 6 |+2 + 3 +0 因此，遵循因式分解，可以将原始方程式变为 （x + 1)（x-2)（x + 2)（2x + 3）= 0

Thanks..good teaching ...nice pace

AWESOME! I'm a math tutor and it's been awhile since I did grade 12 advanced functions; felt like a tool not knowing this

thank you sir. taking differential equations and getting into higher order stuff...somehow i never learned how to deal with higher order polynomials...now i know. Thanks man!!!!

Was about to take a test on simplification of rational equations. Thanks this helped a lot!

tommorow is my linear algebra exam BSCS 3RD SEM AND I am watching it at 3 am. exam is at 8.45 am. and you helped me a lot

Thank you very much ! I was searching for this 😥 Iam so thankfull to you sir !

I LOVE YOU! Thank you sooo much I was really stressing out with a similar problem I had, you really are a life saver! (:

Thanks. This actually helped me. A big help!

you absolute legend! Thanks for the help

@TheKingOfHeartsIV

7 жыл бұрын

you mean The Legend 27?

But guessing the factor takes time...

@DogeFrom2014

8 жыл бұрын

+konda vamshi It does, but I'd always start with +-1 & 2 cause they are mostly factors for every number

@Rohitsurthi7

8 жыл бұрын

+R. W. yeah

@DogeFrom2014

7 жыл бұрын

^ thanks for bumping this into my notifications, really needed to review this as I won't be taking math courses anymore and don't wanna be math-illiterate.

@ashthepandao-o6924

7 жыл бұрын

Mario Micallef you said exactly what my algebra teacher told us xD

Took me until this video to understand this, god bless you.

Instead of doing synthetic division for each of the possible values you can just plug them into the x values in the equation and get the remainder.

@richardhall9815

7 жыл бұрын

Synthetic division is quicker (unless you're using a calculator).

@jojo-nr3yb

4 жыл бұрын

@@richardhall9815 actualy no, i can do synthetic divison in my head and replace the x by a number also in my head. I find that replacing the x is easier to calculate mentally, even though I can do both in my head. However, if you write it on paper, synthetic division is faster, and easier to do since you wont have to multiply as big of numbers, for example in most cases just by +/- 1 or 2

Thank you so much man, that was so helpful!

Really helped me and I watched this video in class before the test and I am ready now thanks

@TheSurya81

4 жыл бұрын

How much did you get in the test BTW

I swear this video helped me thank you so much

Thankyou for this! Finally get it

It helped me solving my daughters assignment..... nice

Super helpful. Thank you very much.

Thank you! This helped me SO much!!! :)

Thank you so much for this!

Thank you very much.. I was in hurry and it gave me clear idea in short time.. Thanks :-)

Good teaching :) thank you!!

For your second example, you can continue the synthetic division for the second and first degree polynomials, right? This is always true I suppose? This way you find the roots -3 and -1\2 and 2 as a remainder so in the end you get the correct 2(x-4)(x+4)(x+3)(x+1\2). Is my thought valid in general?

What if you don't know the factors, so how would you know what you're dividing by. in the first example of synthetic division, you put a -3 because the factor was x+3. but it's not like we're gonna know the factor beforehand, so how would we do it?

@AKhoja

9 жыл бұрын

Kevin Shaik You're right, we don't always know what we're dividing by. The trick is to take the positive and negative factors of the constant term and use those as tests. It may seem inefficient at first, but with practice you'll be able to have intuition on what to do. (Basically, use trial and error)

@Shaikspeare0

9 жыл бұрын

Adam Khoja oh you take the factors. alright. thanks.

would another good way be typing in the formula in the ti 86 calculator and check table and find where the y is 0 and use the x value

so when you factored the 2nd time with the positive 2, that deviser (2) is the factor of 6 right, not 12? I understand that 2 is the factor of both 6 and 12 but say that the question have 2 terms that don't have 2 as the common factor. sorry if I'm confusing, I hope you understand my question, thx

Thanks for the demonstration. I found that making a calculating table in Excel saves you a lot of paper.

Very interesting . Thanks a lot .

thx this method is way better than long division

how did you factor the last part ? after the synthetic division (2x+1)

you are blessing

Thank you! 🙏

thanku this tutorial helped me a lot!!!!!!!!!!!!!!!!!!!!!!!!!!!

In your second example, in looking for the second factor I used -3 instead and still ended up with the right answer. {-3*2=-6} {-1-6=-7} {-3*-7=21} {-25+21=-4} {-3*-4=12} {-12+12=0} Is it possible to have different factors like this, or did I make a mistake in my arithmetic?

Hello can this method be also applied to other polynomial degrees? Thank you

Thank you!!!

Thank you so much.

Thanks, was helpful. (But guessing the factor may take time if the constant term is too big)

Thanks sir .this trik helped me i am very happy

In the first case, dont we have to put a 2 behind de factors? Because of the highest degree number ?

incredible

Thank you soo much this helped me

طريقه رائعه جدا ...nice method

What to do when.constant factors and leadind coefficient factors equal

Thank you!!

thank you very much

Nice video too 💕

find m, and the roots of X^3+mX^2-16X+48 ? :( help?

How do you know if a factor is a root more than once?

can you do that on every degrees?

Really nice, Thanks a lot..

It's really helpful

Great trick Thanks 👍

How did you get 1/2 and 3/2?

Where did you get the -2 from?

is there a way to find the numbers not by guessing them?

Thanks, my textbook didn't even mention the Rational Roots Test!

What's he rational ruths test?

thanks for the help

Does it work for ever? I have a question that it does not workl

Thank you

Am i the one wondering how did he solve the quadratic equations so fast ?

Thanks man!!!

You don't have to do the rational roots test over again--because all the factors of -12 and 2 are included in the list you generated of factors of -48 and 2. So you can use that same list and just ignore the numbers greater than 12.

thank you

Thank you so much😃

how to find factors of m^4-2m^3+3m^2-2m+1=0

Is this method applicable for any degree polynomials?

Thanks man...Helped me much!!!!!!!

you can also plug in the possible factors to the expression, and if it equals to zero, that number you plug in to the expression is a factor. the equal zero simply means zero remainder....just to save you sometime:)

tianxia1wushuang234-天下第一文何文之原帖: Solve fourth order equation of one variable by synthetic division 2x^4+7x^3-29x^2-112x-48=0 Solve: From relationship between root and modulus of polynomials,people know that the roots of the original equation may be "+1-1+2-2+3-3+4-4+6-6+8-8+12-12+16-16+24-24+48-48......" Lucky take -3 +4 -4 -3| +2 +7 -29 -112 -48 | -6 - 3 + 96 +48 +4|+2 +1 -32 -16 + 0 | +8+36 +16 -4|+2 +9 +4 +0 | -8 - 4 |+2 +1 +0 So original equation can be changed into (x+3)(x-4)(x+4)(2x+1)=0 So x1=-3 x2=+4 x3=-4 x4=-1/2 Verify:x1=-3 or x2=+4 or x3=-4 or x4=-1/2 are all the root of the original equation 用合综除法求解一个变量的四阶方程2x ^ 4 + 7x ^ 3-29x ^ 2-112x-48 = 0 解答： 从多项式的根与系数之间的关系，人们知道原始方程的根可能是“ + 1-1 + 2-2 + 3-3 + 4-4 + 6-6 + 8-8 + 12- 12 + 16-16 + 24-24 + 48-48......“ 幸运抽取-3 +4 -4 -3| +2 +7 -29 -112 -48 | -6 - 3 + 96 +48 +4|+2 +1 -32 -16 + 0 | +8+36 +16 -4|+2 +9 +4 +0 | -8 - 4 |+2 +1 +0 因此原始方程式可以变为（x + 3)（x-4)（x + 4)（2x + 1）= 0 所以 x1 = -3 x2 = + 4 x3 = -4 x4 = -1 / 2 验证：x1 = -3或x2 = + 4或x3 = -4或x4 = -1 / 2都是原始方程式的根

Aw. Yes thank you ^.^

Good video

better than my high school teacher..

THANK YOU SIR :D

what about complex numbers?

thanks

Sir how we get 2nd line

good video

Thank u 😁😊

ty love you

Thanks! But what if you don't have a constant term and you can't do the rational roots test?... such as finding all roots for f(x)= 6x^4-5x^3-4x^2

@Farazj7

9 жыл бұрын

then take an x out as a factor

shukriya sir :-)

What if none of the factors work?

Where does the 1 in the last answer

Damn ! It works

So can it happen that there is no factor that will give you the remainder 0?

@mustafarashad7353

7 жыл бұрын

If that happens then that means that the equation that you are trying to simply cannot go simplification anymore.

how would you determine the factors of 6x^4 + 11x^3 - 35x^2 - 34x +k

@jasonophee6153

Жыл бұрын

@@kfjfkeofitorhf9520 this was seven years ago I don't even remember the context in which I asked

solve this 3s^4 + 26s ^3 + 77s^2 + 84^s +24 .. i dont think what u exlained can help me

at 8:42... how did -4 turn into positive 4 which you have wrote into the factor of ( x + 4 )?

@LeedsGoNasty

7 жыл бұрын

-4+4=0

@zain4019

7 жыл бұрын

Ian Paolo Bueno it makes more sense if you think of like this: The factor you chose was 4, so x=4 Now, subtract the 4 from either side and you get (x-4)

@carterreed4676

7 жыл бұрын

Ian Paolo Bueno the multiplier is k {from (x-k)} so if k was -3 it would be {x-(-3)} therefore changing into (x+3)

Why did he use the fractions as one of the possible X

@swetagollamudi6421

10 жыл бұрын

he divided the factors of the constant w/ the co-ef of the variable having the highest power..factors of 12 are 1,2,3,4,6,12.if u divide each with 2, which is the co ef of x^4, u get 1/2,2/2(=1),3/2,4/2(=2) and so on.

why 2x^2+ 5x +3 = (2x+1)(x+3)?

@gouzacastro7293

7 жыл бұрын

FEI GAO this is 2x^2 + 6x + 3.

Plz Factorise: m^4+6m^3+11m^2+6m+1 It is factorising. Plz solve this...!!!

Where does he get (x+3)(x+3) at?

@dayday3597

6 жыл бұрын

You can easily factor x^2+6x+9 using the “x methods” which only works for those equation

what if your polynomial doesnt have factors of the first degree like (x-3) or (2x+1).... take for example x^4+x^2+1... how do you factor this ?

@sk8terman37

9 жыл бұрын

then in the synthetic division problem you would set it up with zeros as place holders for the missing numbers (i.e. if you have x^4+x^2+1 you would set it up with 1,0,1,0,1 if that makes sense. he explained it in the beginning of the video

@damianradinoiu4314

9 жыл бұрын

I did that, but what next ? can you make an attempt to solve it ? you'll see what I'm talking about

@DrMdini

9 жыл бұрын

I'm having the same problem.

@damianradinoiu4314

9 жыл бұрын

Mark Di Nicola it turns out x^4+x^2+1 factors into (x^2+x+1)(x^2-x+1) ,but i have no idea why because it fails the rational root test so it's kinda hard to factor it

@damianradinoiu4314

9 жыл бұрын

by the way, try x^5+x^4+1 also

4x4 + 3x3 - 15x2 + 13x + 16 = 0 please solve this equation