Long Division of Polynomials - A slightly harder example

[mazen1917]

how about if I found this xover3-6xover2-2x+7 by 3x+1

[mollymarie2]

What if there is a number before the first x^4? For example:

5x^4 rather than just x^4.

[patrickJMT]

@mollymarie2 well, in that case, you would divide 5x^4 by x^2; basically though you are doing the exact same thing

[xsergiogx]

how do you decide what power the place holder would be why not 0x4 power or something else please explain because i don't get this part.

[Mavedalicious]

that was really helpful! WIN

[Twighlighw0nder]

@Mavedalicious Can I ask for your age/grade because I'm from the Uk and have just learnt this topic, just curious as to what age the students in the US get taught this.

[Cancer98765]

@Twighlighw0nder

We learn it anywhere from 6th grade to 12th. Yes that is how different our intelligence levels range from... Those poor souls learning in 6th are expected to teach the dumbshits in some schools too..... Personally, I learned it a back in 8th or maybe 9th and keep being expected to know it but always forget.

[Twighlighw0nder]

@Cancer98765 Sixth grade? That's like 11- 12 years old right? That's so ridiculous lol....This is in the first topic for my year one mathematics advanced level course and I'm 16. Sure, it's very very easy but 11-12 years old! I feel so cheated... Then again it is only the first chapter and I can only assume it's in the book to emphasise how fundamental the understanding of polymers/ algebraic factors are. Ok bro, thanks a bunch for sharing. Btw I learnt regular long division at 11.

[Mavedalicious]

@Twighlighw0nder im 15 a sophomore in high school but some kids learn it earlier and some later

[James46776]

Thanks a lot!!!

[WebbTunes]

Thanks!

[guageoooo1]

This helped me out to just remember how. I just skipped to the last part to see what to do with the remainder stuff.. I sorta forgot and all. But i couldn't help but see your reply to someone about not needing that place holder spot... i do think it should be kept there because a lot of people would try to do mistakes that make the answer way wrong. xD Just saying

[FudgeNuts751]

"Uhm" could this count as a home school grade? Or assignment.. I think you should be a online teacher :)

[coolman6566]

hey what if on the outside you have x^2 + 4. on the inside you have 2x^4 - x^3 + 9x^2. do i have to fill in a 0x and a 0 at the end to make it even?

[patrickJMT]

@coolman6566 you do not have to add in anything really. you can add those in though to keep everything lined up. it is just a ' book keeping ' trick

[imurmoma]

do you have to have to have place holders for the other side to?

[patrickJMT]

@imurmoma you dont have to have them anywhere. it is just to make stuff line up

[OhSeeyou]

write my final for me tomorrow please lol

[manam00]

Thankyou so much! you helped me !

[Sunchipper213]

WOW I wish you were my math teacher! Thank you so much for making these videos. It's really very commendable that you would take this much time out to help people with math.. and 1,200 some videos on math is wayyy remarkable. Amazing job!

[bellaaXpattinsonn]

OMG you have no idea how much you've helped me!

Thank you so much <3

[1995sosa]

thank you this was very helpful

[rockfan265]

THANK YOU YOU ARE THE BEST TEACHER EVER

[SureShotStef]

this is really helpful! thanks :)

[geeksquadof1]

THANK YOU!!!!

[patrickJMT]

@geeksquadof1 no problemo

[IsuCycloneFan]

Thanks

[eragon98031]

This equation seems to work perfectly... but what if it's 3x^4 -3x^3 - 11x^2 + 6x - 1 divided by x^3 + x^2 - 2?

Do i take x^3 + x^2 - 2 and add a 0x in there?

[OfficialAla]

is substituting 0 for the missing terms really necessary in these problems or...???

[kyrieleison4]

I always fail in my math exams this year but i'm safe in quizzes and stuff.. but I lost my confidence when the result of the exams came.. I lost it man! But here you are. You gave me hope!!!

[amicrazi]

I have a chapter test in an hour, and this was the only bit I didn't understand, I think you just saved me.

[Wowz4me]

ughh :( i dont know how to do it, my sister doesnt, my parents dont, my teacher doesnt make sense, and i dont get this either :((

[sastido]

college dropout!

[NicholasLiu22]

thank you soooo much, keep making videos!!!

[MrEaglesfan20]

wow you taught me more in 5 minutes than my teacher could in a week

[patrickJMT]

@MrEaglesfan20 come back any time!

[Miguelz82]

@patrickJMT you should get payd :o

[patrickJMT]

@GFXenthusiast that is a good thing! : )

[theselovelygreeneyes]

OMG you saved my life!!!!! Thank you!!!!!

[XxFoster21xX]

thanks helped alot with my homework

[zboi49ers]

Thx bro this video helped me a lot. Good work .

[RudiiJontel]

I'm a math major because of you, Patrick. :)

[patrickJMT]

@RudiiJontel : ) just minor in something useful. pure math is not good for getting a job i think : )

[RudiiJontel]

@patrickJMT the university I'm transferring to has either pure math or math with an emphasis on actuarial science, so I'll probably go with that and maybe minor in physics. I just hope I get a job I'll enjoy like you :) thank you for making these videos, btw; I've been watching for almost a year now :)

[patrickJMT]

@RudiiJontel only do pure math if you are interested in becoming a prof. even then, you can land a prof job easier if do applied math. actuarial science is a good place. stats, computer science are also good!

[RudiiJontel]

@patrickJMT I'll take them all into consideration when deciding at end of next semester! what did you major in??

[patrickJMT]

@RudiiJontel math, of course ; )

[patrickJMT]

@RudiiJontel of course, this is just my opinion!

[graceyjoseph]

wow thanks so much. it actually made so much more sense than my math teacher explaining it. keep posting more :)

[gedevega]

best youtube teacher ever.



[patrickJMT]

@gedevega thanks :  )

[532131]

@patrickJMT Hi Patrick, I just have one tiny question regarding this problem. When do you add or subtract the quotient and the remainder as your final answer? Thanks!

[lordpitt]

This video > my math teacher. Great work dude!

[patrickJMT]

@lordpitt glad you like it : ) 

[ransing3113]

Can you show how you determined what to divide by in order to find roots?

[FreeCultureGuy]

You are better than my regular math teacher. She only gave a simple example, and on the test she gave a more complex like this one.

[benblack25]

eyyyy thanks this helped me out so muchhh

[panterakixass]

I must say, you are a great teacher

[dEViN1887]

so great really helped me out

[patrickJMT]

@dEViN1887 perfect : )

[Votorx]

Excellent video! Just started integration by partial fractions and I couldn't remember how to do long division if my life depended on it.

[profesorsergio]

Great video!!! In Argentina we use a very different way to do this but it is always good to admire how it is done in other countries. Cheers!!!, Prof. Sergio.

[321reball]

fuck you comercials!!! fuckkkk youuuuuuuuuuuuuu

[jezdan141]

thank you so much. my stupid teacher only went over this once really quick and expected us to do like 10 problems over the weekend.

[ahbuanan]

Nice video! It makes me understand after seeing you how to do and I tried it myself before seeing your solution and it works! Thanks a lot !

[itsmeganf]

THANK YOU THANK YOU THANK YOU! My teacher was so confusing when she did this, and the book made it even worse!! Thanks for explaining it!! Thank you Thank you! I feel confident about taking my quiz tomorrow now! thanks so much xx

[joshu2martin]

why didn't you drop the -4 down along with the 1x?

[iseefurtherthanyou]

@joshu2martin he did?

[kari1391]

would you be my teacher? i'll bring you an apple daily! :)

[patrickJMT]

@kari1391 ha, keep watching and i will be

[lekseia]

help!!! x^3 + ax^2 + bx + 12 divided by x-1

[101cutiee]

I wish you taught at my school :(

[preah11]

Thank Yooo <3 Got My Exam Tomorrow And You Helped Me Alot!

[patrickJMT]

@preah11 i hope it went well : )

[skimyhills]

Hi! I just need to check because my answer (I'm the teacher) differs from the book answer. Problem: (x^3 - 4x^2 + 5x - 6) / (x^2 - x + 2) = x - 3 + (6x - 2) / (x^2 - x + 2)

The book answer is just x - 3 but I've done it several times and every time I get a remainder. If you can, just let me know if I win or the book wins ; - )

Thanks!

Beth

[nickrohn93]

@skimyhills My answer was simply x-3, though I imagine it's a week too late...

[buttercado]

thanks for being our teacher! my school doesn't actually teach us so <3

[c1eve1andsucks]

im watching this and im 12, of course i got a headache the first time i saw the problem!

[DoctorJulay]

God Bless you

[farhorizongardens]

I remember watching your videos my sophomore year of high school, and you were a much better teacher than my actual teacher. I would cry because I couldn't do my homework and would do badly on tests, so when I found these videos, I was able to do a lot better! I'm now a senior and I'm taking AP Calc AB and every so often I forget how to do long division since we don't use it often, and I just come back to your videos. Thanks for being awesome. I'll probably still watch them in college!

[Razz27]

Thanks man this really cleared things up for me. And excellent hand writing by the way :)

[jmercer1027]

question what do you do if you have a remainder in the middle of the problem? for example, the problem I am helping my daughter with is 2x^4-3x^3+10x^2+18x+6 / 2x+1 but in the middle of the problem we have 1x^2 as a remainder before we reach the end of the problem... help?

[LordKingfish]

You are a very good teacher! If you're not already one, become one! Even for me, who do not talk English as a mother tounge, it was still easy to tag along and learn.

[RitaMatuck]

Thank you =D

[AutumnxDay]

THANKYOU. :)

[PremiumGaming]

I can learn in a single youtube video what takes at least a week + to do in our current educational system

[razorbladedragon]

thank you!

[UgoPS]

perfect. i now understand what confused me. thanks pat.

[aLiXhottie28]

You are a genius and I love you :) gonna ace these semester exams... hopefully :)

[noobkillar86]

if the numbers on the left r missing a variable do i have to put a zero like if i had to dive x^3-2 (numbers on the left of the square root) would i have to write x^3+0X^2+0x-2 the distribute?

[080594M127]

Hey you should double the equations for people that are advanced in Math.

[ejbalane]

how do you divide a polynomial with two sets of variables

example:

2xy-3x / 3xy^3 + 2x^4

[mattthechamp]

you may have just saved my Math final for tomorrow!!!

[DanaSiew]

woi. thanks

[Narutofan1Pedry]

man i don't know if i might be happy or if i will like to cry, you are such a great teacher, u tought me this in just 5 minutes and 49 seconds what i couldnt learn in 2 hours from my teacher and trying by myself im so happy u are alive, thanks a lot, u got a subscriver an my friends will sub too, i will tell them, thanks again :)

[CaNaDiiAnBaCoN]

youtube > actual teachers.

[SemiAquaticRhino]

@CaNaDiiAnBaCoN cause it's one-on-one, in a sense. in school, it's harder because you have one teacher and about 30 students on average.

[maisiemaisiee]

Really great clear and concise video thankyou :) x

[Iazaldekaxicinho]

I think you make me understand more than my math teacher..

[AVerbene]

it's a shame how a get a better education on youtube than my own school

[pinkmo0n]

thanks! really helped. very clear and simple

[extremesoul666]

Wow you did in 6 mins what my teacher couldn't do all day. Im sure my teacher was being perfectly clear the thing is he moved so fast he didn't consider the fact that some people need to absorb the knowledge first then interpret it.

[mikageaya93]

do you have a video with what to do when the polynomial on the outside has a higher exponent than the one on the inside?

[CindyRoxc]

This made soo much sense thank you so much man!

[ShadowCry01]

Whenever I have a math test, I find your videos to help me :D

[ibuyshirtsonebay]

@zepliveson yes to keep everything in order

[zepliveson]

Question. This may have already been answered, but why do you need to put in the 0x^3? I understand how it keeps everything in order, but does this mean for every time I have a problem like x^2-2x+5/ x^4-x^2.... I actually have to put a 0x^3 in the middle for proper calculation because it would have a proper down grade in powers from the factor 4 to constant?

[lilacjaluba]

thanks a lot for uploading this. great help!

[lilacjaluba]

thanks a lot for uploading this. great help!

[freakable111]

hey great vid man you just helped me pass a quiz... And i am Black!

[bandyjb1]

im only 11 and im not dat good with long division but im totally confuse i keep replayin the vid and still confused

[MrDeviian]

thnks for helping me you are great.

[MrDeviian]

thanks smart man or hidden man now i am smart show your face next time

[88snowbob88]

thankyou so so so much!

[oxijen22]

how can we slved this using synthitic division?

[patrickJMT]

@oxijen22 synthetic division is used when dividing by a linear term

[iamGlitzyGrace]

@oxijen22 well, we can solve this with synthetic division also. It also looks like a polynomial divided by binomial.

Find first the coefficient of each term; then the divisor will be 2 and -5; bring down the first coefficient "1" and secondly the "0"; then you may now continue the procedure. Actually, it's hard to explain it here without any paper. So i'll try to make a video for you :). Remember that, in this case, the remainder should have 2 terms.

[iamGlitzyGrace]

@dtpender i'm sorry but nowadays, i'm still busy for my studies. :)

[valou1128]

And whats wrong with virtual school?

[LightSkinnedMexican]

Thank you i think youll help me pass Honors Algebra II:)

[aafenlared]

I have: 3x^2-4xy+y^2 / x^2+1  do you have any idea of how can I do this?

[samuraigraffix]

awesome i feel much more confident about my math skills thank you sir

[Cougarboy65]

Thanks alot :-)

[mabelle502]

I'm not really getting it what do u do with exponents, when substracting it seems like u r adding and what's the sign. I'm confused!!!

[ClinchMovie]

You are awesome!

[soccerplayaswaggg]

OMG thank you sooooo muchh!

[notafraidtouseit]

in grade 3 i used to do these long division questions that i made for myself and i loved doing it. (Ofcouse there were no integers or powers or square roots). Your just like my old me!

[apoc131]

Did you missed the 0x^3 on purpose when you rewrote the division below?

[ballerforlife666]

thanks!

[theothertube]

Your videos helped me out a ton doing my math upgrading. Thanks.

[SuperChucky69]

Now i can finish my algebra 1 final exam(: i was taking algebra 2, switched schools so i have to take this now to get back in it. 2 months later... So i forgot. Thank you so much. Im only a freshman in highschool

[LightReincarnation]

BLESS YOU!

[inad20120240]

Thank you so much for this video, I wish you were my Pre-Cal teacher!

[Rektek23]

This video is great. This is so much better than my actual Algebra 2 class: good, clear instruction, easy to go back and relook anything I at first didn't understand, and best of :no annoying classmates to bug me while I'm trying to learn. Thanks!

[mymusicequalsmylife]

Your videos have legit saved my grade. Thanks soo much!!!

[FreshBounz]

saved me from another terrible math test! :D

[JuanSneaks415]

You're better than my math teacher! , Thank you.

[tupac0608]

thank you, u saved me from failing :)

[JuanSneaks415]

@tupac0608 ME TOO!

[slittrox]

Thank you so much! you really helped a lot!

[sirkamtep]

thank you

[DVNgirls]

This really helped thank you!

My math teacher gave us a similar problem but she hadn't even taught us how to do long division with a trinomial yet (just binomial) so I had no idea what to do and I couldn't find how to do it (with a trinomial) in my math book so thanks a lot! =]

[rewom6]

That is hardcore.

[jaybee2425460]

im going to dislike this because i dislike math... ugh i feel so frustrated, and lost. i just hate math. 

[scbaldwin13]

Where are you from originally - you said you had a country accent? It doesn't sound it at all in your videos. haha

[z3ro146]

yes yes yes this example saved me from failure thank you so much!!!!

[RasheedAlKotob]

you are a lifesaver ... thanks :D

[ying6342]

Is it possible to divide a trinomial by a trinomial? Ex. a trinomial beginning with x^3...... is divided by trinomial beginning with x^3....... .

[lfo98]

@ying6342 Yes. You'll get 1 (or another constant if you have different x^3 coefficients) + a polynomial divided by the origional trinomial...I think

[lindsey47646]

you screwd up

[brittanyosborne11]

could you please help me divide x^2 + 10x + 29 into x^3 - 7x^2 - x + 87

[lfo98]

@brittanyosborne11 Another way of looking at the question is what times x^2+10x+29 equals x^3-7x^2 -x +87 (you can see this by writing out F=polynomial/trinomial, where F is the answer you are looking for). Looking at the largest powers of x in each, you need to multiply x^2 by x to get x^3, so you know your answer has x in it. You know this is multiplied by the origional polynomial, so do this, and check the difference (subtract) from what you are looking for ( x^3-7x^2 -x +87). Repeat to ...

[lfo98]

@brittanyosborne11 find out what you need to add or subtract from x to get the multiplication to work. If the power of x for the number you are multiplying the answer with (the expression on the left) is larger than the number you are trying to equal to the multiplication (the number on the bottom right) then just add number on the right divided by the number on the left to your answer. Sorry this is long winded, the video explains the steps far better, I just thought Id try to elaborate a bit!

[FailedGearz]

help please! if i have x^3 + 2x^2 - x + 3 / 2x - 1 how do i do it? theres nothing i can multiply 2x by to get x^3

[patrickJMT]

@FailedGearz why not? 2x * (1/2)x^2 works. there are numbers out there besides whole numbers!

[FailedGearz]

@patrickJMT wow thx lol

[PaMS1995]

@FailedGearz hahahhahahahaha

[jhosiah06]

cant hard to understand

[MrLiangaii]

THANK YOU! :)

[vasquezg86]

The whole formula I got. Thanks! But i just don't know why you'd put a 0x to the 3rd to help line up. Why not just solve the problem with out the 0x? How does it help?

[patrickJMT]

@vasquezg86 just try it without the 0x^3

[moo101c]

@vasquezg86 it's just x to the third. not 0.

[TheCanadianGuy08]

@vasquezg86 if you don't account for the x^3 value than you end up missing the -2x in the quoatient and the rest of your quotient will be incorrect. but by putting in the 0x^3 you can account for it.

[Mayranator26]

WHAT happens when there's two variables!

[Bulldogs119]

Mohawk College approves this video :)

Thanks for this.

[3aJeeB17]

Your Are My New God.

[andycao1991]

very awesome , clearly instructed , neat hand-writing . We thank you

[MrWhitnell]

I think you may have just rescued my A level maths, thank you so much :D

[Wigley99]

Much appreciated, mate.

[deathwendz]

please solve this for me ..

2z4-3ax3=2a2x2-2a3x=2a4 by x+a . THANKS <<..

[SamBristolify]

I just want to tank you SO much because I am taking algebra 2 online right now and the guides that they give me to study do nothing to help me and you make it very easy to understand!

[Kelvin838]

amazing video

[ulongkoror]

who needs to pay money for a math tutor when you have this right on youtube?=D