Long Division With Polynomials - The Easy Way!
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- Опубліковано 9 лют 2025
- This video tutorial explains how to perform long division of polynomials with remainder and with missing terms.
Algebra - Free Formula Sheets: bit.ly/3CBeZMY
Polynomials - Video Lessons:
www.video-tuto...
Algebra Final Exam Review:
• Algebra Final Exam Review
Algebra - Free Formula Sheets: bit.ly/3CBeZMY
Polynomials - Extra Lessons: www.video-tutor.net/polynomials.html
I don't understand how we come up with the zeros
Great explanation but, a slight mistake towards the end: (45×)(-3) is equal to -135× and not -145x.
@@mathcollab You caught that as well. Otherwise, good lesson.
Yes , btw 3×45=135 not 145
@@mathcollab its a trick, He's a genius! He will only know that you really understand the problem if you found the mistake!
I was confused from the last problem when i tried it out, but uhm, 3 x 45 is 135 not 145, i even went to use the calculator to convince myself, i was surprised i got the problem "wrong", but it's absolutely fine, everyone makes mistakes sometimes. Keep it up! i'm always ahead of my class because of you!
dude i was panicking trying to figure out where i went wrong
@@VictoriaLeone lol
I see alot of comments saying it was him that was wrong. He was off a little. Unfortunately I learn from examples not concepts so I'll watch a few more and hope the mix up doesn't throw me off
I have never met a math teacher that doesn't slip up on occasion 🤣
yes i got the same answer and freaked out until i read the comments
THIS MAN NEEDS A NOBEL PRIZE FOR JUST BEING THE BEST MATHEMATICS TEACHER ON THIS PLANET
I agree, he deserves an award of some sort.
Agreeeeeed
true i agree
i dont agree without the dont!
🙏🏻youtuber is God favorite
I'm not sure if you're reading this because this video was published 6 years ago but I just want to say thank you. Your videos make me understand everything. seriously can't thank you enough.
i read it and i agree
hes actually still uploading, thankfully
no problem bro, youre welcome man
Second to the past set would be 135 not 145 but great explanation. After following you I was able to catch that. Yay me
Mismoo mali yon pero should not would
@@jasminadriano5160 I don't think she understands Filipino
@@kevingo9348 ay oonga pala
HAHAHAAHHA
@@kristellemilante3844 bakit HAHAHAHAAH
I like how he put “Easy Way” in the title but every video from him is the easy way
@Brantley Drake bots
@Devon Damon where can i find google xD
Uhh, there's an easy way to solve this. Synthethic division is the key, thank me later.
@@giezelvillaluna4647 thanks Captain
@@giezelvillaluna4647 he said it was easy. Bruhuhuhuhuh.
Thank you so much. I didn't understand it when my teacher was going over it but after I watched this video I found it so much easier to do. Thanks!
He explains it way better than any of my math teachers did, why cant teachers be like him? Thank you so much! I thought i was really stupid at math but it turns out i needed the right teacher
But I still don't understand
@Alex Nicole But it turns out that everyone learns differently, leaving nothing understood by teachers (at least in the long run).
learnt more in 12mins of him than the entire month of my math teacher
@@DrillGMusicbecause you can pause and rewind this maths teacher.
@@HeartShapedBox93yep, some teachers might be bad, but these comments make it seem like their teachers might as well not exist, which is unrealistic LOL
Even if the teacher is bad u will still absorb some things…
If your teacher has never made a mistake while teaching you, he is not a good teacher. Thanks, boss, great video.
My teacher must be incredible because she makes a mistake every 20 seconds
@@reezy9727 😂
what does making mistakes have to do with being a good teacher lol? Maybe if a teacher can't admit mistakes it correlates..
@@mickeyp6639 true cuz teacher basically know their mistake
That means my high school physics teacher is a brilliant teacher because she did addition and subtraction first before multiplication and division
Thank you so much organic chemistry tutor ! I've been stuck for so long but just the first 1:54 mins saved me
I’m currently in in ODE and have learned this every single year for 6 years now, and I still never remember it. This and synthetic division are one of those things you assume will never come up again, but has come up every single math course I’ve taken so far in my undergrad. Turns out a big part of finding general solutions of second order differential equations is finding the roots of a polynomial.
I just finished my bachelors in Mechanical Engineering, and remember having to look this up about 2.5 yrs ago which was when I took Dif Eq's lol now trying to remember bc as a side hustle Im tutoring HS Math
if only synthetic divison with coef of x where there.@@mikem9270
10:50 , 45 times 3 is 135 , I got so confused there I multyplied multiple times and at last used a calculator , it is 135 , mistakes happen , else it's all great , keep up the good work
Same, I multiplied a lot of times but still get 135
Same, i got too confused lol
Thanks! I thought I made a mistake (pretty common) lol
yeah. he made a mistake.
I had the same problem, but we all make mistakes
This makes so much more sense when you talk about how stuff goes together and how to do it instead of a teacher telling you to just do it
You are the most amazing math tutor on UA-cam! You have an incredible talent for making the math look so easy. I just wish my math teacher explained things as well as you do. Please keep making these videos, because I will need to take a ton of math courses to major in Biology.
As far as I know, biology doesn't need much math--but math can train you to think critically and analytically, which is certainly an important skill to have if you're a scientist.
Thank you naliwanagan na ako ngayon hayst thanks lord
@@kinanradaideh5479 you really don't need much other than basic algebra, but if you major in any biological science you tend to have to take a bunch of math classes to get your degree. I'm a pre-vet animal science major and I have to take everything from college algebra to advanced calculus to graduate, but I'll likely only need basic algebra once I'm actually in the work field
@@cassimmons1613 true i am in computer programming currently taking college algebra and you def. need the basics to pass the class
@@anunknownperson4018 you need more than the basic algebra if you're going to do computer science. In fact computer science is one of the most maths intensive courses. You'll basically be in the department of maths doing computer science
Thank you for doing it step by step, Most teachers would just assume that students will know what is happening.
Tbh ,This has to be the best and easiest way of doing division of polynomials,thanks alot for saving my life as I have polynomials exam tomorrow!!
It took me 5 minutes to get it,, and I'm usually a slow learner
Thank you so much! Saved me 8 pages of work
Omg narancia
It took you 5 minutes I wish I could be like you
I should’ve just saved my money instead of enrolling from school....I learned more from you than my teachers
Me too
HEYYYY NCTZEN!
@@LookImGrapeNoseBoy HEYYY GHORL!!! Who’s your bias?
@@hyucks_moles6397 My bias is Nct 127 is Mark, Johnny, Haechan, WinWin, Yuta, Jaehyun, and Taeyong. The rest of the members are my bias wreckers lol. For the other subunits, I bias all of them but my ults are Shotaro, Hendery, and Xiaojun.
@@LookImGrapeNoseBoy oohhhhh well my very ult is Haechan and in WayV my bias is YangYang, 127 is Taeil and Dream is Chenle but for Nct U i’d say it’s Shotaro. Just like you they’re all my bias wreckers😭
No matter how many times my teacher could tell me how to do this, I wouldn't be able to understand it. There's just too many people in my class for one person to individually help. Thank you for this! You're gonna save my grade big man :)
You are literally my trig teacher rn. I am doing remote school and my teacher does not send notes to his online students, so I am relying on you heavily to teach me the material. You do such an amazing job, thank you so much!!!
0:19 समाधान : x²+५x+६÷x+२
ˍˍˍˍˍˍˍˍˍˍˍˍ
x+२)x²+५x+६(x+३
x²+२x
﹋﹋﹋﹋
०+३x+६
३x+६
﹋﹋﹋﹋
०
I'm also doing online university after 15 years and heavily relying on him for a lot of material 😂. Just out of curiosity what are you studying?
Noob
I literally learn from this compared from my teacher's discussion and the modular examples
My teacher didn't discussed abt this
I did too.
true
learn more*
2025 ANYONE??? Man, I left so confused when I saw this in the lesson thank you so much!!! 💜
You are wayyyy better than Khan academy!
Yessss
agreeeeeeeddd
Agreeeeeeeeeee
On what basis did you make the comparison? Khan Academy explains mathematics quite well where TOCT fails to do so, he just shows the process without really explaining why it happens.
@@meownamejeff I get what you mean. But TOCT explains the process way better than Khan Academy (for me at least).
I am generally really good at math, but my grade has been dropping (for reasons I won’t state). This channel is pretty much going to save my grade lol
Edit: It didn’t. But this channel has still been super helpful.
Do you need help , I can assist with whatever work you need it for
Hope u recover from ur downsides in life :>
@@azyle2104 7:35 i need help why did he add 0x3 and 0x
@@blazeworm1759 okay so imagine that a formula always has to LOOK complete
x⁴ + 3x³ + 2x² + x + 1 = 0
This looks very complete , right ? There's no x to a certain power missing .
But if you look at this example :
x³ + x + 6 = 0
In a way, it looks incomplete because the x² is missing ... but hey ! We can write in a way where we can bring the x² in the equation AND the initial equation will still hold true
We do that by making the coefficient of the x² WE ARE INTRODUCING , 0 ... so 0x²
So that 'incomplete' equation will now become :
x³ + 0x² + x + 6 = 0
And of course 0 multiplying anything, is still 0 .. thats why the equation still holds true
@@blazeworm1759 in the video's example , the equation looks incomplete because we dont have an x³ or an x ... so he introduces it in the equation by the way I just told you
11:08 I guess you miscalculated the 3 x135=145,it should be 135,its totally fine...your still the reason why I kept learning math,physics,chemistry...
I agree with everyone else you are an amazing teacher thanks to you I passed algebra 1 and now I’m on algebra 2 and of course I’m viewing your videos to get by!!! I will be passing along your videos to my classmates!!!!
I’ve started to love math because of you! Thank you so much for sharing your knowledge!!
0:19 समाधान : x²+५x+६÷x+२
ˍˍˍˍˍˍˍˍˍˍˍˍ
x+२)x²+५x+६(x+३
x²+२x
﹋﹋﹋﹋
०+३x+६
३x+६
﹋﹋﹋﹋
०
God bless you sir 🙏🏻. Because of you, I am getting this down. I’m in an online college algebra class and it’s been a long time since I did Math so I’m relearning and learning new concepts without any help from the professor. These videos are invaluable despite when created. Many blessings your way and for all learning these concepts. Keep at it!
Thank you for this! I have a test tomorrow and I didn't know how to do long division with polynomials and this really helped.
Anybody still watching in 2024?
Yepppp
Yep studying for midterms
Why not dude? I always find my self coming back here. I was done with this long time ago tho. I don't wanna lose it so i keep refreshing my mind.
@@yousufabdirazakkhader3827 I agree and I am also still watching
@@Tactyoh same but for finals
bro this guy is a genius and great at explaining things!
dude you taught this more clearly in 12 minutes than my teacher did in the span of 5 days
Say that again
My teacher taught us this thing under 20 minutes while mocking us, and yet we still don't know because it happened too fast.
This is literally the channel on youtube
shut up keep there's plenty of good (even better than this one) channels explaining synthetic division and math in general.
Are you two talking in a different language?
@feathersss this is the funniest comment thread I have seen. I don't even remember commenting this and why was that yosef guy so heated..
@@sha1_________________54 probably plays fortnite....
Yosef I know your comment was from a year ago but why were you so pressed?
teacher got to this by the end of class and i was so confused. first few minutes of this video cleared everything up. thank you!!
Thank you! I was getting really frustrated with my teacher's notes, I didn't quite understand what she was saying and the terminology was leaving me really confused. Found this video and it all came together and clicked. I am extremely grateful, and hope this will help me out in my online class :D
Which grade are you in?
I'm in grade 7
I just want to take a moment to say that I friggin love you man lol, you are absolutely the best teacher for me!
Even getting the question wrong he explained better than most teachers
that proves how bad some teachers are i think they should be teachers for pre school if they aren't good at explaining
45*3=135
Ya I was so triggered
😘
I was so confused when I see that
-9x
-54x
= -63**
@@chiechiedayon7519 -9 - (-54)
Great simplicity in explaining math! By far, the best math tutor in UA-cam!
no doubt about it
fr
Thank you for going slow and explaining these concepts so well! You're fantastic.
your voice is so healing ☁️✨☀️🍃🍂
what does that mean
something about the combination of the hushed voice tone, the pauses and the black background makes me feel like this is something secret I'm not supposed to know how to do
U just saved my life brother. A true one.
Thank you for explaining!! I learn this better with you than my lecturer 😭 you're a life saver thanks!!
Thank you I really needed this video for my algebra class!
for some reason this is the hardest thing for me but you explained it well, maybe my brain will finally retain it
I love how you are not vague with your explanations, like, you spend time explaining every step.
After watching this video I think that my maths teacher should take maths classes from this man .
I don't know what's the reason behind making a sum so hard to understand.
But all credit goes to you for making it easy 💗
You really know why students have a hard time understanding the principle behind it. Your explanation is excellent.
7:16 why when you but the numerator you add 0x*3 and then 0x , someone help please
10:50 I think its wrong 45.-3 =-135 NOT -145
you can also use 0x^4 + 0x^3 + 0x^2 + x - 3 as the divisor instead. It wouldn't affect the answer.
bruh, i wana know if you found the answer xd. did you pass exams?? ahahha
@@meownamejeff
Is it okay not to put zeros in the expression?
same please someone answer
@@prettyalina7237 Still waiting for an answer. lol
7 years ago and still beneficial. this guy is awesome
His voice is so calming I already feel like a can accomplish math.
facts
Thank you for this saved me so much time and stress finally someone who explains it very amazing i was struggling on this topic!
Thank you!!!! Taught better than my teacher for sure! So helpful!
To real, watched this only bc I didn’t get my hw at all and this made me understand it so much better
Great video and a really good format for teaching, thank you a lot and 135 :)
6x*3 + 18x*2 + 45x +135 + 423/x-3 (* means to the power :) )
thanks we have the same answer
No ^, means to the power of, * means multiplication
Use ^ for powers
6x³+18x²+45x+135+423/x-3
yayy we have the same answer
Cant go wrong with the organic chemistry tutor. This video was made 6 years ago but it still helps!
dude teaches better than my teacher
I have a feeling you are going to save my life man :) Don't trip about the 45*3 mistake your videos are still awesome nobody makes perfectly calculations every single time !!
The best tutor, I've come so far because of this guy and his Chemistry, Physics AND some Math. We all appreciate ur efforts. Hoping u find a tutor in ur life like we found u in our life :D
-Best wishes and thanks again.
0:00 Divide Multiply and Subtract
2:46 Subtract
6:57 Divide 6x to the 4 minus 9x squared plus 18 divided by x minus 3
hi i know you left this comment a year ago but im confused as to why he put 0x cube
@@Ye0nj1_ hi it is a placeholder! there was no x cube term in the polynomial but there was an x^4 and an x^2 term so we had to add the x cube between them. there can be an x^3 term in the answer even if the original equation doesn't have an x^3 so we need that placeholder
Second to the last set is 135 not 145 ...but good literally best youtube math tutor lots of love🤞🏿
I'm studying abstract algebra, I had to check back how to do this when dealing with factorization of polynomials over a field 😂
Great video
This really helped me out a lot. Thank you. I subbed!
At this point start tutoring teachers how to teach, they have a lot to learn from you!
ur the goat, you explain every step so quickly and effectively. Can't thank you enough.
You're very good at explaining.. But u can always use calculator when multiplying 45x3..no need to be shame on it.. everyone makes mistake.. keep it up sir.. ur vids are way clear than any tutorial I've watched on youtube ..no intro, direct to the point... Students like me tend to click/choose shorter tutorial ... Ur channel was introduced to me by our mathematics teacher in CVSU-CCAT in Philippines, Ms. Judi Gonzales .. I'm thankful, and Grateful she did that ...if it wasn't for u I won't be able to pass our Midterm..
It's 2023! is anybody still watching?
Wow, my class learned better from you than me! Thank you.
ur the best Mr ao!
11:10 it’s actually 135x not 145x
fantastic, really helpful videos. My online course videos are terrible compared to these. Great job
4th year in engineering, and I still come back to this video. Goat.
Who here in 2024 watching for exam review ??
Are grade 7 ??
Mehh
You know it
This guy is better than Khan !!
This guy is the goat , explains stuff so effortlessly and simply
Anybody watching in 2023 with their crying ass rn
Relateable.
I was so confused with my calculator how 45 * 3 =145.. it all because I trust you more than my calculator... Great work sir... thank you
I had the same question
Who's watching this in 2024?
Me
I am watching it in 2016 brotha
Here
Me
me
3 * 45 = 135 not 145
PaleBlueDotCitizen got confused for that omg i thought my calculator is broken. LoL
Right I was also like...can I trust this dude lmao
I love how after trying to get this for a week i still couldn't and my teacher couldnt get me to understand too, after 2 minutes of watching this i understood everything
Anybody watching in 2025???
Yes
Anybody still watching in 2024
It's the day after Christmas and I have exams in January, so yeah I'm still watching 🤧
Always
Your literally a godsend bc my teacher did 5 practice problems and I didnt understand but the first time u said do it on ur own I got it correct 😭
anybody still watching in 2023?
Wait , isn't the last one :
6x³+18x²+45x+135+423/x-3 ?? Just a quick doubt :) Great explanation btw 😄11:52
Yes, you’re correct! That’s supposed to be the final answer but since he made the mistake of using 145 instead of 135, it made his answer wrong 😅
Nothing too big though! Just a small mistake anyone can make ^^
no
yes
Just wanted to say thanks for all the chem and ha2 help 🔥
Sir you made a mistake in 10:43 because 45 x (-3) is 135, not 145....
its not even 135 its -135 lol
the final answer is 6x3+18x2+45x+135+423/x-3
also I respect the fact that their is an actual human who saw that mistake
Can you make some videos with more complex division? I understand this but I'm having trouble applying it to more complex problems.
Bro I was so stupid before this video 💀 You've made my life easier man, thanks
Anybody still watching in 2027 😮😮
Are U living in the future?😂
@@lordjay111nah he just wants to come back in 3 yrs
That was 3 years ago lil bro
11:27, it is actually 135x, not 145x. Doesnt matter, i understand the principle anyway. Thats why the next number is wrong to, it should be 405.
I cannot describe my gratitude towards this person for making this video. I’m a sophomore in honors Algebra 2 and I joined the class late since I took geometry over the summer and they took a while to transfer my classes. It’s been difficult because my class is a lot faster paced than my class freshman year since this is an honors class so sometimes I struggle to understand what my teacher is talking about but this video saved me like hours of confusion!!
Anybody watching in 2025
Still watching at 2024?
Thankyou for teaching me long division.
Anyone still watching in 2049?
anybody in 2025?🎉
You're one of the best teacher on UA-cam
Anyone watching in 2023
This is not the video for that
I honestly don’t understand what happened at 7:55 where did the 0x^3 and 0x come from. That threw me completely off.😪
Me too lol...
*Searching for the ans in comment section*
Yeah you add the 0's because in the problem there was no number that had x^3 and 0x, so you add them as filler.
@@krisha_panchal but why?
@@jeff8966 if there is no place holder then you won't be able to solve the problem, you can't subtract x^3 from x^2, therefore you have the place holder x^3-0^3
you still don't get it ? or do you get it now ? lol 1yr later