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!
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.
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.
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 😭
+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!
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.
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
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.
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
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 :)
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.
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!
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!
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!
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!!!!
Well, in that equation, you would factor out an x giving you x(x^2-4). Then you could factor the x^2-4 into (x-2)(x+2) giving you x(x+2)(x-2). Then set them equal to zero and get the zeros, -2, 0 and 2.
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.
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
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
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!
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.
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
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.
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!
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!
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!
thank you so much for your videos, i was absent the day this lesson was taught in my class and my friends' notes did NOT help me in the slightest. this really is a lesson that has to be taught verbally
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!
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!
This fit nicely in with my adv functions class right now. I missed a week of school getting knocked on my ass by a virus. Factoring was always a weak spot and then this came along... Thanks again!
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!
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.
THANK YOU SO MUCH my teacher really doesn't know how to make me understand this stuff... i've learned this so much easier in like 10 minutes from you than from a whole month of school with my teacher! really, thank you (:
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!
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
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.
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
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
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 :)
You are a baller! i like that factoring when you had a coefficient "3" in front of you're x^(2) trial an error at a glance ;).. keep up the good work! This video taught me well
@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!)
i'm a little upset right now because my teacher had us go through a whole bunch of steps to find the zeros but you kept it simple and to the point lol thank you. I was a little confused at first bet this video helps.
@coolman6566 As said, there are no roots for it, but if you want to simplify it you could use substitution and put x^2=u, then you will have u^2+6u+9. Solve it, you'll get it simplifies to (u+3)(u+3). reverse the substitution gives: x^4+6x^2+9 = (x^2+3)^2
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
@MeistyMan007 yes, when you plug the equation into a graphing calculator, it will give you your points on the x-axis(zeros) then you can use one zero to use synthetic division and find the irrational roots
Thanks, no this ib student can catch up! Also thanks for that little shortcut to make trail and errors much shorter, that my teacher never showed!!!! Well thanks u lefty!
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!
patrickJMT can you group factor the polynomial you get after you plug in 1 to find the other factors??
2x square
5x square
3x-18
We learned it differently...instead of finding f(p/q) = 0, we tested p/q with synthetic division to make sure we got 0 as a remainder
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.
+Slikver The Wise tru
To be fair, doing taxes doesn't take a whole semester to learn nor does learning about a 401k.
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.
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.
you don't know how to do taxes cause ur an idiot
This guy has so much confidence in himself to use a Sharpie for math 😭😭
Madlad
Facts 101
Wdym?
@@twicelovesonce1004 Confident to not make any kinds of mistakes in the paper.
@@twicelovesonce1004 confidence to not make any mistakes, you can’t erase with sharpe if you didn’t kno 😂
This is 8 years ago but it’s still more helpful than my teacher.
Same for me but 10
But now 11 years ago lol
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 😭
your views must skyrocket right before exams
Tyler Topulos i’m glad you pointed that out lol
Tyler Topulos my math exam is tomorrow 😖😂
Angeluz Lopez same
I always question life when I do problems like this..
honestly can't thank you enough. this cleared up so much
+Geraldine Wijesundera glad i could help ya out
+patrickJMT What if you don't have a constant? Like 3x^4 - 5x^3 -3x^2
+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!
+Viktoria Hart Thanks!This really helped on one of my problems.
Is there a video on sketching functions?
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.
Each problem takes 10 minutes and I have a whole page of these problems to do. Fml
Just factor bra
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
you mean an hour each
Binary Number: Pay me $100 to solve 1 problem. I would totally do it. That's the way I would view this!
Exactly
i like how people say there is an easier way to do this yet they fail to inform us how
^ lol ikr
Calculator
caramel5000 Explain how you do this with a calculator alone?
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 True. Another way is to graph the function on some calculator or by hand to determine the zeroes from there.
Your videos are going to go on for several generations and continue to save lives. Haha thank you.
TheRandoy yes buddy. I am watching this in 2018.
2019 here, buddy. Common, guy what you doing all the way back in 2018?
@@kakurocksman 2020, what are u doing back in 2019
@@poopa.c6 2021, what are you doing in 2020?
@@mattkrasnecki4458 2022, we’re still here
super happy i could help a random guy from sweden! i would love to visit there one day
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
+Anthony Esposito happy I could help you.
I really appreciate the fact that you explain a week class just in ten mins.
Thanks ...
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!
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
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 :)
you explain this better than my algebra 2 teacher!!
my pleasure :) glad my videos could help you out
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.
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!
My teacher should just put links to your video on her website cause she legitimately cant explain this stuff to save her life. Thank you!!!
You just saved my life. Online, I just can't stand the way my professor lectures. THANK YOU!
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!
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!
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!!!!
Well, in that equation, you would factor out an x giving you x(x^2-4). Then you could factor the x^2-4 into (x-2)(x+2) giving you x(x+2)(x-2). Then set them equal to zero and get the zeros, -2, 0 and 2.
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.
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
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
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!
Thank you so much man! Thanks to you I got a 93 on my Precalc Final.
Luis Santos good work
It has really helped me so thank you.
hello sir your videos are really helpfull for me to do my math assignment in school
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.
....sorry - if understand the basic principle it should not be confusing.
I just learned this 100% better in 10 minutes than 2 weeks in my precalculus class. Thank you
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
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.
Not all heroes wear capes. Thank you, Sir!
i wear one around the house, they are quite fun and comfortable. no more drafts.
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!
10 hours before my Differential equations exam, not worried. I got my man Patrick teaching me this stuff.
Great... studying for my CSET, haven't done math in 5 years, this is a great refresher! Thanks!
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!
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!
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!
thank you so much for your videos, i was absent the day this lesson was taught in my class and my friends' notes did NOT help me in the slightest. this really is a lesson that has to be taught verbally
Patrick! I studied with your videos and got a 98% on my test!! Thank you!!!
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!
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!
YOU'RE A LIFE SAVER. I'M STUDYING THE NIGHT BEFORE THIS MATH TEST!
This fit nicely in with my adv functions class right now. I missed a week of school getting knocked on my ass by a virus. Factoring was always a weak spot and then this came along... Thanks again!
You and people like you are going to help me pass my precal test. Godspeed, sir.
oh my god thank you!!! i have a Precalculus test tomorrow, you are a life saver !!
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!
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.
This was more helpful than learning it from my teacher. Thank you!
THANK YOU SO MUCH my teacher really doesn't know how to make me understand this stuff... i've learned this so much easier in like 10 minutes from you than from a whole month of school with my teacher! really, thank you (:
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!
+wowazowgirl my pleasure! glad i could help ;)
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
thank you so much for clear explanations, all the examples you solve there are so easy to understand and simple
Thank you for making such clear and simple videos. Wish me luck on my midterm in an hour.
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.
Right
Thank you I was up for hours trying to figure out how to do this and your video cleared it right up
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
@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
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
Dude, I greatly appreciate this lesson. I couldn't find any way to understand it, but this made it so easy. Thanks!
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 :)
man, this video is more useful than the remainder theory and synthetic division video
you have made algebra much easier for me thank you
You are a baller! i like that factoring when you had a coefficient "3" in front of you're x^(2) trial an error at a glance ;).. keep up the good work! This video taught me well
@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!)
My professor is russian and her accent is so deeeeeeppp this helped me so much thank you so much!!!!!!!
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
i'm a little upset right now because my teacher had us go through a whole bunch of steps to find the zeros but you kept it simple and to the point lol thank you. I was a little confused at first bet this video helps.
This just helped me study for a test I have to pass.... Thank you!!!
Thanks Patrick! You did good job helping me...I am really appreciated.
OMG I FINALLY LEARNED THE TECHNIQUE! THANK YOU FOR THIS!!
Your explanations are absolutely great. Thank you so much.
@coolman6566
As said, there are no roots for it, but if you want to simplify it you could use substitution and put x^2=u, then you will have u^2+6u+9. Solve it, you'll get it simplifies to (u+3)(u+3). reverse the substitution gives: x^4+6x^2+9 = (x^2+3)^2
This really helped with my College Algebra homework! Thank you!!
OMFG you're so good, I hope all teachers are like you. Sadly, all of them are nothing like you.
Great video! I lost the notes from class and your video helped the most compared to others
Bronies, Bronies everywhere.
Thank you! I cant believe im barely studying at about 3 in the morning, but this helped me so much!
Thank you so much. Have a test tomorrow was worried but now i think im good to go.
College algebra final tomorrow you are my savior!!!!!!!!!!!
who else loves this guy? such a life saver
You are the best youtuber for maths tutorials ✌🏻🙏🏻
My concept got cleared
This is super helpful! Thank you so much for posting this. It makes everything so much easier when it is explained.
you sir have saved me a lot hairs from stressing out so much, thanks!!
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
happy i could help :)
it is a long and tedious process but that's how it goes
@MeistyMan007 yes, when you plug the equation into a graphing calculator, it will give you your points on the x-axis(zeros) then you can use one zero to use synthetic division and find the irrational roots
Youre such a great help
I got an exam tomorrow. Just subscribed :)
Thanks! This helped me with my pre-calculus.
I'm here with 100% satisfaction. Great sir 🙏
thanks, that was the best video explanation I've found on this!
Most helpful vid i have found in the whole day.
give this guy a medal
legendary!!
Thanks, no this ib student can catch up! Also thanks for that little shortcut to make trail and errors much shorter, that my teacher never showed!!!! Well thanks u lefty!
Thanks a lot for breaking the process down. Now I understand the Rational Root Theorem better. :-)