❖ Finding all the Zeros of a Polynomial

❖ Finding all the Zeros of a Polynomial - Example 3 ❖

Рет қаралды 1,399,805

14 жыл бұрын

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Example 2: • Finding all the Zeros ...
Finding all the Zeros of a Polynomial - Example 3. In this video, I use the rational roots test to find all possible rational roots; after finding one I use long division to factor, and then repeat! Very fun!

Пікірлер: 858

@patrickjmt 5 жыл бұрын

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

@lorenarzadon9758 4 жыл бұрын

patrickJMT can you group factor the polynomial you get after you plug in 1 to find the other factors??

@wolverine2511 4 жыл бұрын

2x square 5x square 3x-18

@hmmyes443 8 жыл бұрын

I don't know how to do taxes, or how to sign up for a 401k, but thank christ i know how to find the zeroes of a polynomial.

@emmaclare0 8 жыл бұрын

+Slikver The Wise tru

@ducksoop.x 7 жыл бұрын

To be fair, doing taxes doesn't take a whole semester to learn nor does learning about a 401k.

@patrickjmt 7 жыл бұрын

agreed josh t. but i also agree strongly with slikver. i think it should be required for students to take a class on basic finance including loans, taxes, retirement plans, interview skills, etc.. The stuff all of us will use in life. I am not sure how important many of the topics taught in algebra are.

@ducksoop.x 7 жыл бұрын

patrickJMT I agree. I feel like we should have more choice with our courses in High School. Algebra was important for me since I am a CS major and math will not be going away anytime soon. But I'm sure for the majority of people it's not necessary. There should be one course that just teaches you how to (properly) adult. Taxes, loans, retirement plans, interview skills, social skills, etc. Real life skills. I learned about taxes inside and outside of High school. Had an economics class. To be fair it was mostly a blow-off class. Many would also argue that the parents should teach these things. But in some instances.... Maybe they don't have parents or their parents aren't very knowledgeable on those things either.

@tomi9062 7 жыл бұрын

you don't know how to do taxes cause ur an idiot

@catherineyi 4 жыл бұрын

This guy has so much confidence in himself to use a Sharpie for math 😭😭

@gigatrooper5098 4 жыл бұрын

Madlad

@MyfamilyJenkins 4 жыл бұрын

Facts 101

@twicelovesonce1004 2 жыл бұрын

Wdym?

@JRusselNV 2 жыл бұрын

@@twicelovesonce1004 Confident to not make any kinds of mistakes in the paper.

@louj8112 2 жыл бұрын

@@twicelovesonce1004 confidence to not make any mistakes, you can’t erase with sharpe if you didn’t kno 😂

@milan4989 5 жыл бұрын

This is 8 years ago but it’s still more helpful than my teacher.

@zmoosky 3 жыл бұрын

Same for me but 10

@deepakthapa1587 2 жыл бұрын

But now 11 years ago lol

@lovelypersonn1720 2 жыл бұрын

Nah fr I got an F on my homework cause I did this shii wrong but after watching this video I wanna cry at how much I understand him more than my teach 😭

@astroctopus9500 10 жыл бұрын

I always question life when I do problems like this..

@tylertopulos5943 7 жыл бұрын

your views must skyrocket right before exams

@arianahi 6 жыл бұрын

Tyler Topulos i’m glad you pointed that out lol

@angeluzlopez5813 5 жыл бұрын

Tyler Topulos my math exam is tomorrow 😖😂

@dandrejohnson1522 4 жыл бұрын

Angeluz Lopez same

@myufruit4770 8 жыл бұрын

Each problem takes 10 minutes and I have a whole page of these problems to do. Fml

@jayman4581 8 жыл бұрын

Just factor bra

@JM-lh8rl 7 жыл бұрын

josabad munoz However, some polynomials can't be factored with conventional rules and you need to use the test and divide to find the zeroes. But totally, factor if there's an obvious root that saves you the trouble of doing this

@Oscar-gx2yf 6 жыл бұрын

you mean an hour each

@ti84satact12 6 жыл бұрын

Binary Number: Pay me $100 to solve 1 problem. I would totally do it. That's the way I would view this!

@treyon9190 5 жыл бұрын

Exactly

@geraldinewijesundera1700 8 жыл бұрын

honestly can't thank you enough. this cleared up so much

@patrickjmt 8 жыл бұрын

+Geraldine Wijesundera glad i could help ya out

@steamdecknation7908 8 жыл бұрын

+patrickJMT What if you don't have a constant? Like 3x^4 - 5x^3 -3x^2

@ViktoriaMom 8 жыл бұрын

+foreverX ransford You can factor out an x squared first: so then it looks like: (x^2) ( 3x^2 - 5x - 3 ) that means that x^2 = 0, so you have x = 0 as a zero, and it has a multiplicity of 2 (meaning that particular zero showed up twice as an answer.) Then, use the quadratic formula to find the zeros of the rest.good luck!

@PhuongTran-yq8mj 8 жыл бұрын

+Viktoria Hart Thanks!This really helped on one of my problems.

@Emk315 7 жыл бұрын

Is there a video on sketching functions?

@TheRandoy 10 жыл бұрын

Your videos are going to go on for several generations and continue to save lives. Haha thank you.

@swapnilbankar6913 6 жыл бұрын

TheRandoy yes buddy. I am watching this in 2018.

@kakurocksman 5 жыл бұрын

2019 here, buddy. Common, guy what you doing all the way back in 2018?

@shahema.3447 4 жыл бұрын

@@kakurocksman 2020, what are u doing back in 2019

@mattkrasnecki4458 3 жыл бұрын

@@shahema.3447 2021, what are you doing in 2020?

@Alexj_movieguy 2 жыл бұрын

@@mattkrasnecki4458 2022, we’re still here

@patrickjmt 12 жыл бұрын

super happy i could help a random guy from sweden! i would love to visit there one day

@AlexLanyu 9 жыл бұрын

i like how people say there is an easier way to do this yet they fail to inform us how

@milkgg1394 9 жыл бұрын

^ lol ikr

@caramel5000 6 жыл бұрын

Calculator

@ilikealotofthings731 6 жыл бұрын

caramel5000 Explain how you do this with a calculator alone?

@evanurena8868 5 жыл бұрын

TacocatBackwards Well, their is Newton's Method, which is one quicker alternative to finding the zeros of a polynomial function, instead it utilizes calculus. Another is Descarte's rule of signs, but involves no calculus.

@rogueonparmer4870 5 жыл бұрын

Newton’s method doesn’t always work though. It’s good when it does but if you have a point where f’ =0 then you can’t use it anymore

@patrickjmt 11 жыл бұрын

being able to find the zeros of a polynomial is a fundamental problem in mathematics; many real problems can be stated in this form and the solutions are then the zeros. i agree, not everyone in the world is going to use this. in fact, a small percentage will. however, that small percentage are people doing (to me) cool things: building bridges, computer science and programming (you like the internet, i bet), studying infectious diseases via statistics, the list goes on and on.

@pandareiko6756 2 жыл бұрын

Thank you, I've been looking high and low for a video that would teach me how to find the zeros of a polynomial with a degree higher than 3, and this really helped me out! Keep doing what you're doing, you're a massive help :)

@zabiiaryan8325 6 жыл бұрын

I really appreciate the fact that you explain a week class just in ten mins. Thanks ...

@IceTactics 10 жыл бұрын

You just saved my life. Online, I just can't stand the way my professor lectures. THANK YOU!

@yaxomoxay 8 жыл бұрын

I love you!!!! lol. Seriously, thanks, I spent two hours reading the book and the notes and I couldn't figure out what to do after the first synthetic division. Outstanding work, great explanation. You are the man.

@anthonyesposito8076 7 жыл бұрын

thank you man. No joke 1 minute and 25 seconds into this video it explained more that my online class professor who leaves a lot of steps out. Appreciate it

@patrickjmt 7 жыл бұрын

+Anthony Esposito happy I could help you.

@lovemusicunapologetically6245 10 жыл бұрын

Thank You so much Patrick...You helped me in college and now that I just graduated I want to say..You are the best math teacher ever

@patrickjmt 12 жыл бұрын

my pleasure :) glad my videos could help you out

@incitepurity1468 7 жыл бұрын

you explain this better than my algebra 2 teacher!!

@juliehadley8336 7 жыл бұрын

I know this video is a bit old now but I still want to express my gratitude. You helped me out a lot tonight with my homework and I truly appreciate it. Thank you!

@icoowater23 9 жыл бұрын

I never knew how to do the ones with the rational zeros because i skipped math the day we leanred them.. thank you so much for dedicating your time to upload these videos!!!!

@sandersforfree3098 10 жыл бұрын

Dude, I greatly appreciate this lesson. I couldn't find any way to understand it, but this made it so easy. Thanks!

@xobeenaxo 8 жыл бұрын

This is super helpful! Thank you so much for posting this. It makes everything so much easier when it is explained.

@chriskolta5615 7 жыл бұрын

God bless your soul... you cleared up everything and i just went to about 6 other videos and none of which could explain this concept like you did. THX

@lovebaxter 10 жыл бұрын

so helpful and straight to the point and you show the best techniques and its so easy to follow because u explain it all! my teacher didnt teach us anything like this and it was so hard for me until i watched this and now i can do my homework!! thank you soooo much

@eyebean5511 8 жыл бұрын

omg this helped so much. I can never understand what my teacher is teaching, but then when I watch math videos they make everything clearer. thanks so much!

@CaveSpiderNinja 6 жыл бұрын

Honestly you deserve an award my good sir. Math test tomorrow, missed review day and looking at the packet I was so confused until I found your video. Cheers!

@shamshodmahmadiev2273 8 жыл бұрын

thank you so much for clear explanations, all the examples you solve there are so easy to understand and simple

@huntereberhardt9910 6 жыл бұрын

I just learned this 100% better in 10 minutes than 2 weeks in my precalculus class. Thank you

@emiglam 11 жыл бұрын

Thank you for making so much sense! I was recently home sick from school for four days and pretty much had to fend for myself as far as learning the lessons I missed. Thanks to your videos, when I came back to school and aced the quiz on everything I missed.

@Milesz17solo 12 жыл бұрын

I have independent studies for a while and I have to learn on my own and I've been learning everything all thanks to your video, thank you soo much!

@ethanhawn9536 8 жыл бұрын

Thanks! This helped clear this up completely. Had everything I needed to know for my quiz. :)

@xPrOtOgHaNdIx 10 жыл бұрын

This was more helpful than learning it from my teacher. Thank you!

@Mozzarella98 10 жыл бұрын

Thank you! I cant believe im barely studying at about 3 in the morning, but this helped me so much!

@madeyeatreides4055 5 жыл бұрын

Thank you I was up for hours trying to figure out how to do this and your video cleared it right up

@wowazowgirl 8 жыл бұрын

This is SO much more understandable as a method than what we are being taught to do in class. Thank you so much. You just saved me from having to re-take a class next year!

@patrickjmt 8 жыл бұрын

+wowazowgirl my pleasure! glad i could help ;)

@christicrawford8055 6 жыл бұрын

Your explanations are absolutely great. Thank you so much.

@ryanmccaldwell 10 жыл бұрын

this video was infinitely helpful. I can't even express it. haha thanks so much. I've watched a ton of videos about this already but you made it plain and simple. fantastic job.

@vandomog5971 6 жыл бұрын

Patrick JMT. Ignore all - ve comments as I've found this tutorial a great help. This will really help me in the future, when I am trying to factor and then state the zeros of cubics and higher degree Polynomials. By the way, if it wasn't for people like you, who give up their free time to help others with their Mathematical issues, then we'd all be worse off, so to speak. Thanks. Dominic

@BrownBrotha 13 жыл бұрын

Thank you so much, I have a test tommorow and its been three weeks since the unit started and i have learned so much stuff about polynomials its insane. I used all your videos that I needed for review and I have an even better understanding! Thank you for the great explanations, great hand writing, and great videos. Keep up the good work :)

@eXBouncers 6 жыл бұрын

This is a great explanation! It will definitely help me on my test this week! Thank you!

@jenn9212 4 жыл бұрын

this helped so much!!! i have watched so many other videos here on utube ab how to find the roots of quartic functions but only this has helped me n i feel a lot more confident on how to find the zeros of quartics thank u so much

@patrickjmt 4 жыл бұрын

happy i could help :) it is a long and tedious process but that's how it goes

@zobekguerrero1366 7 жыл бұрын

That's cool You're left handed! I was born left handed but 2 years of training with my off hand I became ambidextrous. Left handed power!

@savannah2323 8 жыл бұрын

Wow thank you so much. I was struggling with this and your video made it crystal clear to me

@luissantos5090 8 жыл бұрын

Thank you so much man! Thanks to you I got a 93 on my Precalc Final.

@nickd.2449 5 жыл бұрын

Luis Santos good work

@revincentiii 9 жыл бұрын

I have watched several instructors and this is one of the best demonstration as he does not waste time. If you understand the best principle it should not be confusing. I have watched them over and over to arrive at the principle being taught.

@revincentiii 9 жыл бұрын

....sorry - if understand the basic principle it should not be confusing.

@joker5266 12 жыл бұрын

Great... studying for my CSET, haven't done math in 5 years, this is a great refresher! Thanks!

@mederkutbidinuulu7396 10 жыл бұрын

Thanks Patrick! You did good job helping me...I am really appreciated.

@555gleerocks 2 жыл бұрын

Thank you so much I was like I’m going to fail this class and have to take it again you broke it down to where I can understand it

@iluvsmokeythecat23 11 жыл бұрын

I had so many ppl try to explain this to me... but I just sat there saying yeah... your video really helped me understand how to do these problems now! Thank you so much!

@jaydawilliams4785 7 жыл бұрын

This really helped with my College Algebra homework! Thank you!!

@Pegisus2501 9 жыл бұрын

Thanks a lot for breaking the process down. Now I understand the Rational Root Theorem better. :-)

@wyclifferichards3533 8 жыл бұрын

thanks alot pato!!!! that really helped a whole lot, big up!!!

@ThelVadlee 5 жыл бұрын

YOU'RE A LIFE SAVER. I'M STUDYING THE NIGHT BEFORE THIS MATH TEST!

@PearlAlex 11 жыл бұрын

I've gone through all three of your "Finding all the Zeros of a Polynomial" examples. I have a math test tomorrow and this has been helpful :) thank you!

@jynnilin 11 жыл бұрын

You are so great! Thank you so much for this resource!

@ricelover796 6 жыл бұрын

you can also plug the equation into the calculator and check the x intercepts to make the problem easier to find the possible roots and solve using synthetic division. This is so helpful!

@guilelessnocturne 11 жыл бұрын

Wow, thank you so much for making this video. I just learned this in class this morning, and I was the only person in my class who didn't understand the lesson. This video was incredibly helpful. You either explained it much better than my teacher, or I was still half asleep when he taught it to us. :) Again, thank you!

@livingliferight502 12 жыл бұрын

Dude, ever since I started watching your videos my grade went up from a C to a B in Pre-Calculus. No lie. You make things sooo much simpler!! I LOVE YOU!

@jeanchauvin1877 6 жыл бұрын

This is perfectly what i needed to learn. Thank you so much. :* please upload more. :)

@TheHairwaytoHeaven 11 жыл бұрын

You have no IDEA how excited I am!!! I am doing online College Algebra (teaching myself basically) This was amazing! I've asked multiple math majors and this video explained it in the best way possible to help me!!! THANK YOU SOO MUCH!! I might just pass this test!

@Th3SmartAlec 11 жыл бұрын

Thanks man. I was absent from school last Thursday when we learned this and you know how helpful the math textbook is when explaining things...anyway, thank you for your help!

@vegnitte3068 3 жыл бұрын

OMG I FINALLY LEARNED THE TECHNIQUE! THANK YOU FOR THIS!!

@Lydia774 4 жыл бұрын

Thank you so much!! I was on verge of breakdown, but now I get it! Hopefully my test tomorrow goes well...

@ericawolfe1445 8 жыл бұрын

Dude, you are better at teaching than my professor is. I cannot express how thankful I am for your videos, and how angry I am that my university chose to hire someone who cannot speak english or dictate coherently.

@michellea2741 10 жыл бұрын

Thank you!! I needed this refresher!

@straps001 10 жыл бұрын

Great video! I lost the notes from class and your video helped the most compared to others

@EliteNz3 10 жыл бұрын

Bronies, Bronies everywhere.

@glassapple727 9 жыл бұрын

Thanks! This helped me with my pre-calculus.

@nicollelandaverde2762 8 жыл бұрын

This just helped me study for a test I have to pass.... Thank you!!!

@themostunluckykid 10 жыл бұрын

Thank you for making such clear and simple videos. Wish me luck on my midterm in an hour.

@thakurrajsingh665 7 жыл бұрын

You are the best youtuber for maths tutorials ✌🏻🙏🏻 My concept got cleared

@utte12 12 жыл бұрын

Patrick, thank you very much for helping out and sharing your knowledge. u rock! you rock for many reasons but especially cuz of the fact that you explain something thats very complicated (according to the books with all their confusing notations), in a very simple and understandable way :) I don't excel in maths so well, but you're making it possible for me! thanks /// random guy from sweden

@brittsyoutoob 12 жыл бұрын

thanks, that was the best video explanation I've found on this!

@jonathanhenrikson8290 6 жыл бұрын

This was very helpful! Thank you! My math teacher is way too smart so she has no idea how to dumb it down to a standard I can understand! Keep these vids coming 😜

@markmartir1923 9 жыл бұрын

Most helpful vid i have found in the whole day.

@SomVTambe 6 жыл бұрын

Thanks Patrick for such a wonderful video!

@patrickjmt 6 жыл бұрын

you are most welcome :)

@mrkidofminecraft 10 жыл бұрын

I had to know this! Thank you sooooooooooo much!!!

@njunguisidonie4721 Жыл бұрын

It has really helped me so thank you.

@flynig1 14 жыл бұрын

These video are a gift thank you!

@bekiyigzaw2381 3 жыл бұрын

You made my day I swear you make it clear

@fadhll 12 жыл бұрын

YOU ARE FANTASTIC !!! u and your lectures always save my life!!!!! I don't know how to thank you.. Again, Thanks for sharing your knowledge with us as students. Your my best teacher and tutor EVER

@sudipdas1390 5 жыл бұрын

Thanks for taught me this thing so easily🙏

@cazmayt2886 7 жыл бұрын

Youre such a great help I got an exam tomorrow. Just subscribed :)

@kaiwalker5886 8 жыл бұрын

Instead of finding all factors of zero by hand use a graphing calculator and put the function in, then go to the table and type in a value for x using a number from rational zero theorem. If it is a zero the y value will be zero. This is so much easier then guess and check by hand.

@knockhello2604 5 жыл бұрын

Right

@gumi_twylit2605 6 жыл бұрын

Thank you so much for a clear explanation!!! You can now be my teacher in Math!!! 😄😄😄

@patrickjmt 12 жыл бұрын

@jeleemay97 yes, it is very time consuming. to find zeros of a polynomial is actually a deep and important concept.

@patrickjmt 13 жыл бұрын

@MrChainsawmanic1 factor it (it is a difference of perfect squares) ; you should be able to factor it twice using the difference of perfect square formula! (that is the hint i give you!)

@emthesheep9728 4 жыл бұрын

thank you so much! Such a useful and clearly explained solution! :)

@SonOfaChipwich 11 жыл бұрын

You and people like you are going to help me pass my precal test. Godspeed, sir.

@mariahadams9068 8 жыл бұрын

Thank you so much!!! It helped a lot!

@999saleh999 12 жыл бұрын

@patrickJMT look man . you're the best !! for the first time in my all exams Iget full mark .. Thank you from the depths of my heart

@GDBroy 11 жыл бұрын

Thank you, Patrick. Thank you.

@212Sima 11 жыл бұрын

oh my god thank you!!! i have a Precalculus test tomorrow, you are a life saver !!

@melindam.3856 8 жыл бұрын

Bless your soul I understand my math lesson now

@corrinerox 11 жыл бұрын

maths was my favourite subject school - i was getting close to 100% from year 9 to year 12 but then I got pressured to do pharmacy and pharmacy in australia is by far underpaid compared to the US so I have reverted my career to medical statistics (biostatistics) - i have used your video patrick as well as khan academy to help me revize my maths - thanks for all your help. i havent done maths for over 12 years