Finding All Zeros of a Polynomial Function Using The Rational Zero Theorem

This precalculus video tutorial provides a basic introduction into the rational zero theorem. It explains how to find all the zeros of a polynomial function by using the rational zero theorem and by factoring polynomials. The rational zero theorem helps you to identify the first zero by listing all possible rational zeros and then evaluating the function to see if it's equal to zero at that particular value of x. This video also explains how to find all zeros of a polynomial function using synthetic division. You need to know how to factor trinomials and how to solve quadratic equations using the quadratic formula. This video contains plenty of examples and practice problems.
Introduction to Polynomials:
• Polynomials - Classify...
Polynomials - Basic Operations:
• Polynomials - Adding, ...
Dividing Polynomials By Monomials:
• Dividing Polynomials B...
How To Graph Polynomial Functions:
• How To Graph Polynomia...
Intermediate Value Theorem:
• Intermediate Value The...
_____________________________________
Long Division - Polynomials:
• Long Division With Pol...
Polynomial Long Division - More Examples:
• Polynomials - Long Di...
Synthetic Division of Polynomials:
• Synthetic Division of ...
Remainder Theorem & Synthetic Division:
• Remainder Theorem and ...
Factor Theorem & Synthetic Division:
• Factor Theorem and Syn...
Rational Zero Theorem:
• Finding All Zeros of a...
______________________________________
Real & Imaginary Solutions - Polynomials:
• How To Find The Real &...
Solving Polynomial Equations - Synthetic D:
• Solving Polynomial Equ...
Solving Polynomial Equations With Excel:
• Solving Polynomial Equ...
Writing Polynomial Functions Given Zeros:
• Writing Polynomial Fun...
Descartes Rule of Signs:
• Descartes Rule of Signs
Solving Polynomial Inequalities:
• Solving Polynomial Ine...
_____________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 583

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor Жыл бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzread.info/dash/bejne/poamssixgpjOXdo.html Functions and Graphs: kzread.info/dash/bejne/jIh52JqInqrHqNI.html Transformations of Functions: kzread.info/dash/bejne/pq2FrtJvqJCtn7g.html Graphing Polynomial Functions: kzread.info/dash/bejne/pIODx8idobDcpKQ.html

  • @user-xh5we2wi5z

    @user-xh5we2wi5z

    4 ай бұрын

    I enjoy your lecture

  • @norvin7410
    @norvin74103 жыл бұрын

    This guy is saving millions of students from failing. godbless this dude!

  • @rutii.a6428

    @rutii.a6428

    2 жыл бұрын

    Amen! He saved me too.

  • @roblominmus

    @roblominmus

    2 жыл бұрын

    I legit have a test on this topic tomorrow, he just saved my grades.

  • @absolute6422

    @absolute6422

    2 жыл бұрын

    He’s a literal god send

  • @mekdestsegaye9825

    @mekdestsegaye9825

    2 жыл бұрын

    Amen

  • @erikduzelljr

    @erikduzelljr

    Жыл бұрын

    Dude yeah. I'm taking online course and the explanations from professors suck. This guy explains simply and slowly so my dumbass can understand. Thank you!

  • @xkt-jz9dx
    @xkt-jz9dx4 жыл бұрын

    Watched him from high school and now graduating with an associates all the way with him. Now it’s my turn to teach my little sister with his videos :)

  • @JW-oi4mo

    @JW-oi4mo

    2 жыл бұрын

    well, this is wholesome

  • @UNKNOWN-bp8it

    @UNKNOWN-bp8it

    2 жыл бұрын

    @@JW-oi4mo Agreed.

  • @al-khatabalshibli393

    @al-khatabalshibli393

    2 жыл бұрын

    well thats cute

  • @nataliecampos5888

    @nataliecampos5888

    2 жыл бұрын

    Bruh my brother yells at me.

  • @Zeshal_asmr

    @Zeshal_asmr

    2 жыл бұрын

    Nyc trick... 💜

  • @breadedlemon7067
    @breadedlemon70673 жыл бұрын

    I like how he doesn’t edit out his mistakes nor does he retake his recordings, it always feels like he does these videos in one go

  • @morriscallahan3549
    @morriscallahan35493 жыл бұрын

    I just spent 2 hours in a lecture and had no idea what the rational zeros theorem was, but then I watched your video and it takes 10 seconds to learn it. thank you.

  • @user-xh5we2wi5z

    @user-xh5we2wi5z

    4 ай бұрын

    Mmmmm that's amazing, in 10 seconds

  • @abigaellejoseph8701

    @abigaellejoseph8701

    19 күн бұрын

    I literally just stopped showing up to lectures cause it feels like a waste of time. I don't learn anything

  • @mpc7440
    @mpc74403 жыл бұрын

    There is a 100% chance that i will never use this for my nursing degree lol

  • @googlewebsite5953

    @googlewebsite5953

    3 жыл бұрын

    prbly not but ive heard theres a surprising amount of math involved in nursing

  • @twomarinesandadunce1107

    @twomarinesandadunce1107

    2 жыл бұрын

    Hey, a fellow nursing major using this bs

  • @bopiiq8947

    @bopiiq8947

    2 жыл бұрын

    honestly same

  • @jaybirdeclipse3971

    @jaybirdeclipse3971

    2 жыл бұрын

    Fr- as a future Vet/poultry science student(working on community College classes to go less into major debt lol) I'm never going to use this crap

  • @emberphoenix3039

    @emberphoenix3039

    2 жыл бұрын

    Lol I want to go into an artistic career and I feel the same way. 🤣

  • @Arthur-th4rm
    @Arthur-th4rm5 жыл бұрын

    As someone that has a professor that has a terrible accent, and it's impossible to understand anything he says. You are a life saver. I really appreciate your videos, thank you.

  • @daviemeister3355

    @daviemeister3355

    4 жыл бұрын

    Yeah, I severely hate when that happens! Its not that I dislike those teachers... they are really nice! The problem is that their accent does not just suit the job in which they are teaching! Are we all so for diversity that we forget that its not about how diverse the teachers are but how they get the point across to the students? I am doing quite well in advanced functions right now.. I had a teacher with terrible accent, so not only do I not naturally understand her, but I naturally tune out when its impossible to comprehend. I had to search and search on my own, just to keep up. I just hope you were able to do well in that class...

  • @mohamedwael566

    @mohamedwael566

    4 жыл бұрын

    Lol, same for me

  • @Em022

    @Em022

    Жыл бұрын

    CC life in Seattle

  • @hannahdadoll5008
    @hannahdadoll50083 жыл бұрын

    I was about to have a breakdown when I decided to open my KZread and search for tutorial, thank God I found this. This is a big help for someone like me who had a modular class. Thank u so much

  • @sparrow9735

    @sparrow9735

    3 жыл бұрын

    Same. I was just about to give up. Thank god I found this😭

  • @notsofiasco

    @notsofiasco

    3 жыл бұрын

    I'm still having a breakdown because I still can't understand because I am THAT dumb😭 I badly need a personal tutor😭

  • @arc1671
    @arc16714 жыл бұрын

    should've done a problem that's first term was something other than a 1.

  • @jacebrowy1420

    @jacebrowy1420

    3 жыл бұрын

    Agreed but it still helps

  • @1nonlytorres757
    @1nonlytorres7573 жыл бұрын

    "make sure this is a zero, if not, something is wrong" that scared me bruv. lol

  • @tylerdruskoff9689
    @tylerdruskoff96893 жыл бұрын

    It’s 1am and a school night. This hw is due tomorrow. Thank you so much

  • @tmerkury2813
    @tmerkury28136 жыл бұрын

    World's best tutor

  • @Angeloyoutube835

    @Angeloyoutube835

    4 жыл бұрын

    Right. I’d rather have this guy as a teacher instead of my current one.

  • @velsiz6217

    @velsiz6217

    3 жыл бұрын

    Seriously

  • @jeibi6483

    @jeibi6483

    3 жыл бұрын

    Ikr, i feel like i owe this guy my life😳

  • @luisdiamante5541

    @luisdiamante5541

    3 жыл бұрын

    Hes already got a high amount of subscribers just in 6 months! Before he was 500k+ subs. Now hes already 2M!!

  • @ireallylikehuskies9472

    @ireallylikehuskies9472

    3 жыл бұрын

    amen

  • @ghw024
    @ghw0246 жыл бұрын

    Hey I've been watching some of your calc videos and just wanted to say thanks for all the help, you are legit saving me from failing tomorrow, thanks!

  • @BrothersorTerraria

    @BrothersorTerraria

    6 жыл бұрын

    Goodluck man!

  • @sogeqt9188

    @sogeqt9188

    5 жыл бұрын

    just wanted to say that this is an Algebra 2 concept

  • @chekzz5352

    @chekzz5352

    4 жыл бұрын

    @@sogeqt9188 its present in cal, precalc, and sometimes in algebra 2

  • @Manny24_8

    @Manny24_8

    3 жыл бұрын

    @@sogeqt9188 I didn’t have it in my algebra 2 course lmao

  • @randommonkey4900

    @randommonkey4900

    Жыл бұрын

    @@sogeqt9188 i never learnt it in alg2 just learning rn in precal

  • @chair1694
    @chair1694 Жыл бұрын

    This is a pretty consistent way of factoring high degree polynomials, there's no weird algebra manipulations, and it's very repeatable

  • @mindmate0
    @mindmate05 жыл бұрын

    why do you always sound like you are kidnapped and forced to make tutorials great video nevertheless

  • @natckwan

    @natckwan

    5 жыл бұрын

    so we can get high marks on our test

  • @manalibisht6865

    @manalibisht6865

    4 жыл бұрын

    do u want him to act like a clown or something

  • @sora_is_my_dad420

    @sora_is_my_dad420

    4 жыл бұрын

    It factors the polynomials or else it gets the the hose again.

  • @ravenreyvillacastin6264

    @ravenreyvillacastin6264

    4 жыл бұрын

    He makes it because he cares , and why the hell would you care about his voice when you can learn more from him bro? He saves all the students in my school because our teachers are lazy , so we thank him on how he takes effort making these videos we dont have blank answers on our exams👎👎👎

  • @MrStrutxD

    @MrStrutxD

    4 жыл бұрын

    unfunny, stop trying to be.

  • @ToBreatheMusic
    @ToBreatheMusic2 жыл бұрын

    I am pursuing a psych degree through an online university and currently taking a math course. I have been stuck on this topic for about an hour now and began to feel very defeated. I watched your video, and a light bulb went off in my head. A million times thank you!

  • @Gegajim
    @Gegajim3 жыл бұрын

    This voice introduces peace to my brain

  • @Yummycinnamonroll

    @Yummycinnamonroll

    2 жыл бұрын

    Istg

  • @nitamac1312
    @nitamac13126 жыл бұрын

    YOU ARE A MATH ANGEL!!!!

  • @oneandonlyjet3622
    @oneandonlyjet36224 жыл бұрын

    I would be like most others and say I'm watching your videos because my teacher sucks, but I for whatever reason fall asleep in my calculus class. Thank you for making your videos informative while remaining to the point. Doubt you'll read this, but thank you. Have a great day! :)

  • @abeehamakhi5148

    @abeehamakhi5148

    4 жыл бұрын

    The same exact thing happens with me. I try so hard not to but alas it still happens and THESE VIDEOS R A BLESSING.

  • @c0da625
    @c0da6253 жыл бұрын

    You’re a good teacher!!! Your videos are helping me with my maths. Thanks a lot man!!

  • @azuce2860
    @azuce28602 ай бұрын

    this is the best channel existing in the entire youtube, thank you so much

  • @blackenwhite6190
    @blackenwhite61909 ай бұрын

    I've been watching for 2 years now and just wanna say thank you so much this is really helpful

  • @sarahdemonia5591
    @sarahdemonia55912 жыл бұрын

    Thank you! I have a calculus pretest in a few days and this concept panicked me--but this video allowed the idea to come back to me and I am not as afraid anymore. Thank you!

  • @averyleahy6268
    @averyleahy6268Сағат бұрын

    I love you sir...I was on the brink of tears before finding this. Bless you.

  • @bltoliver13
    @bltoliver134 жыл бұрын

    Definitely buying some merch after my final, you've saved me throughout my entire pre-calc class

  • @willw4096
    @willw4096 Жыл бұрын

    1:50 "The purpose of the Rational Zero Theorem is for us to get the first zero, and then use that to get the others using synthetic divison."

  • @VTINE00
    @VTINE005 жыл бұрын

    for the last two answers (the square ones) could you simplify them in any way or are they just written like that?

  • @CheatCodeSam
    @CheatCodeSam5 жыл бұрын

    always look for your videos when I have a problem in math. you got the best math videos on the net

  • @user-rv4ep1bs2p
    @user-rv4ep1bs2p8 ай бұрын

    i PRAY for you all my brothers and sisters who struggle may the LORD bless you with knowledge and understanding ASK and you shall recieve in LORD JESUS NAME AMEN!!!

  • @stickshiftstarship
    @stickshiftstarship2 жыл бұрын

    My instructor had us list all factors and try synthetic division over and over, your way is so much simpler! Thank you!

  • @lolerishype

    @lolerishype

    Жыл бұрын

    I suppose that method is technically more straightforward; but Organchem’s method is indeed faster.

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    MR. Organic Chemistry Tutor, thank you for an extraordinary introduction to the rational zero theorem. This powerful theorem explains how to find all the zeroes of a polynomial function.

  • @LifeWithJB1
    @LifeWithJB12 жыл бұрын

    God bless this man fr…some of our math teachers don’t teach and just give the work but now I am understanding it!!!

  • @jylztimothyacoba8463
    @jylztimothyacoba84633 жыл бұрын

    So happy to have this type of teacher, i always understand his lessons this 2020......

  • @allawayn1005
    @allawayn10054 жыл бұрын

    Idk how I appreciate this. you’re phenomenal

  • @elainel7503
    @elainel75035 жыл бұрын

    thanks so much, you did it much faster and easier than other tutorials

  • @Starwarp02
    @Starwarp024 жыл бұрын

    Thank you, your video helped me learn a section the professor skipped over but was still needed for the final

  • @kokolin5876
    @kokolin58764 жыл бұрын

    Thx for the saving my ass entire high school year

  • @emperorshaggy7190
    @emperorshaggy7190 Жыл бұрын

    You really just explained everything math teacher has been trying to teach the class for the past 3 months in less than a half hour

  • @caribbeankpoplover
    @caribbeankpoplover2 жыл бұрын

    I watched this man’s videos when I was studying Engineering Math in university and now I’m watching him again to teach my students 😊

  • @Fusion4Dayz
    @Fusion4Dayz4 жыл бұрын

    I use your videos for linear algebra (eigen values / eigen vectors). Thank you so much!

  • @serenashynemae
    @serenashynemae Жыл бұрын

    Hi I just want to say your video toturials are amazing I easily get it

  • @jeffreybrasier794
    @jeffreybrasier7942 жыл бұрын

    I can't tell you how much I love your videos. You have countlessly saved my life from failing

  • @Melisa-oz6kb
    @Melisa-oz6kb6 жыл бұрын

    YOU'RE SERIOUSLY THE BEST TUTOR EVER

  • @alhassanmichael306
    @alhassanmichael3062 жыл бұрын

    In fact, you are helping a lot of people. May God bless you.

  • @rosiewoodland23
    @rosiewoodland23 Жыл бұрын

    Thank you so much, I've been struggling with this concept and you helped me tremendosly!

  • @Thorite_Gem
    @Thorite_Gem9 ай бұрын

    This video is far more helpful than my professor was. Thank you so much!

  • @blacktutor16
    @blacktutor16 Жыл бұрын

    please what if the coefficient of x^3 is not 1? will u multiply it by the coefficient or find their factors separately?

  • @person-cf3di

    @person-cf3di

    Жыл бұрын

    kzread.info/dash/bejne/iW2DpNOwYq2yoKg.html this video explains it

  • @brysongummerus6481

    @brysongummerus6481

    Жыл бұрын

    Find factors seperately

  • @jayjoetenry7656
    @jayjoetenry76565 жыл бұрын

    Thanks for the help man im in algebra II and this is really helping me

  • @sebe1015
    @sebe10154 жыл бұрын

    That second example was exactly one of my exam questions. Following your steps, I ended up getting them right before I watched how you solved for them. Thank you!

  • @purplejam1470
    @purplejam1470 Жыл бұрын

    Question about the first example, how did the -5x turns into ±3? (In the introducing example thingy)

  • @user-ls2vf1sh5z
    @user-ls2vf1sh5z4 ай бұрын

    Had to pause at the second part, but did get the answer right. It's easy and manageable if you just take enough time to find the factors and stuff, very helpful.

  • @IsabelRodriguez-nv2ue
    @IsabelRodriguez-nv2ue3 жыл бұрын

    Thank you so very much. All your video lessons are great!. Thanks again!

  • @jacebrowy1420
    @jacebrowy14203 жыл бұрын

    I have a test today and I knew nothing so I watched a ton of ur vids on what I was learning and it helped a lot so thank u and pray I do good on my test

  • @kingmac0058
    @kingmac005810 ай бұрын

    U teach better then my teachers u talk at a pace I can understand u

  • @juanguzman41
    @juanguzman415 жыл бұрын

    Can you use the method used to find the first zero, to find the others?

  • @cerulean22b69
    @cerulean22b693 жыл бұрын

    Ok this is way simpler than the ALEKS explanation, also I find your voice kinda calming, I like the calm way you explain everything it really helps cause I'm cramming again and super stressed right now.

  • @jeanettegomez9984
    @jeanettegomez99844 жыл бұрын

    Learn a lot from your videos! Can you please make one with function table of fog gof fof etc.? Thanks!

  • @TheReal4th
    @TheReal4th4 жыл бұрын

    I don’t need to use the descarte’s rule of signs right?

  • @seff2451
    @seff24517 ай бұрын

    im taking my final exam today and I can proudly say you pulled me through this course every single week without fail

  • @sommers8355
    @sommers83554 жыл бұрын

    thank you. i had forgotten how to do this and it was a great refresher!

  • @ahmadfarisnurmohdmazlan5532
    @ahmadfarisnurmohdmazlan55323 жыл бұрын

    Thanks for the guide man, really need it. Wish me luck. Have an exam 2 hours from now.

  • @djdesad
    @djdesad4 жыл бұрын

    Thank you for the handy videos, allow me to get better preparation in college algebra.

  • @fin07
    @fin076 ай бұрын

    this is helping me out immensely, thank youuuuu 😭😭

  • @limitzlol7274
    @limitzlol7274 Жыл бұрын

    i just learned like a whole chapter of math that i had no idea what was happening in, in legit 2 minutes like one example and i get it thank u sm

  • @alicebloomfield4295
    @alicebloomfield42952 жыл бұрын

    This made my life so much easier!!!! Thank you so much 💗

  • @anastasnikolov9396
    @anastasnikolov93964 жыл бұрын

    Nice explanation, you could use Horner's method right from the start instead of plugging in the values manually. It would save you ton of computation and you would end up with new coefficients right when you find the root so it saves you some time. Still very nice video :)

  • @seynawynn4974
    @seynawynn49742 жыл бұрын

    By far my favorite KZreadr!!!! Thank you !!!

  • @D0nkkkkkk
    @D0nkkkkkk5 жыл бұрын

    Love you man. Best on KZread.

  • @lenborghini392
    @lenborghini3925 жыл бұрын

    This is so very helpful.. thanks man

  • @ME-sz6fw
    @ME-sz6fw3 жыл бұрын

    Thank you for teaching me what my teacher could not

  • @kristine6519
    @kristine65195 жыл бұрын

    this helped me so much! thank you!

  • @WhoTFMadeThisChange
    @WhoTFMadeThisChange2 жыл бұрын

    I love you so much man, I can’t focus in class for some reason so you’re a saint to me

  • @Fiendnat138
    @Fiendnat1383 жыл бұрын

    im on differentials and i needed a refresher, thnk u sm!

  • @tutstorial8474
    @tutstorial84744 жыл бұрын

    would it still work for degree 4 above or degree 2 and less?

  • @yk.hav3ndobs.4
    @yk.hav3ndobs.42 жыл бұрын

    anyone know what to do if the polynomial had a misisng term so you had to do a 0 has one of the terms in standered form?

  • @minerxd1427
    @minerxd1427 Жыл бұрын

    Question! do I need to do the synthetic division part or am I good with just the x = 1?

  • @srlaila
    @srlaila3 жыл бұрын

    Excellent. Thank you very much. What do you use to write on screen please?

  • @reic.2748
    @reic.2748 Жыл бұрын

    How did you get the 3 in the first equation

  • @thelastsonofuranus7078
    @thelastsonofuranus70784 ай бұрын

    For the 4:13 problem, can someone please explain how he got the letters next to the coefficient after he did synthetic division? I am horribly lost.

  • @_nottheankles7218
    @_nottheankles7218 Жыл бұрын

    hi i just wanna ask, can u still use the rational root theorem without a constant?

  • @faithfowler7484
    @faithfowler74842 жыл бұрын

    So what would you do if the leading coefficient isn't 1?

  • @thenerdyqt7534
    @thenerdyqt75344 жыл бұрын

    Thank you so much. I know what to do on my quiz now❤️❤️🤗

  • @LoganDaBro
    @LoganDaBro2 жыл бұрын

    Thank you so much for this channel... Truly a lifesaver

  • @rutii.a6428
    @rutii.a64282 жыл бұрын

    Thank you very much! this video helped me a lot. God bless you!💙💙

  • @juliana6353
    @juliana63534 ай бұрын

    What if q is like 4 and p is 3, would I just use the common factor of +- 1?

  • @findx9402
    @findx94025 жыл бұрын

    Thank you so much your vids all ways help

  • @charlestheanimator1676
    @charlestheanimator16763 жыл бұрын

    when you edit your videos can you check your audio levels so that they are hitting -12db as a peak and averaging between -10 db and -12 db on average? If your not sure how to do this I use your videos all the time and am willing to do it for you no charge. I just want to not have to max my speakers out to only hear you faintly still lol.

  • @donisaac5789
    @donisaac57893 жыл бұрын

    10:58 what if my b is already negative? Does it transform to positive or does it stay negative

  • @hersyhersy6171
    @hersyhersy61713 жыл бұрын

    Yo, just askin, what if the constant term happened to be 1? Is it factorable if the mid coefficient is higher than 1?

  • @aprilbernabe7563
    @aprilbernabe7563 Жыл бұрын

    Can anyone tell me why in the first synthetic division problems he said to take the inverse of the x= to start, but in the possible zeros example he took the actual x= value and started that way.

  • @idwpercy
    @idwpercy5 жыл бұрын

    just wanted to say thanks, you are explaining tons of math in a way that will allow even my dumb ass to pass my exam tomorrow

  • @mercy5551
    @mercy55515 жыл бұрын

    u explained it better than my professor thank u

  • @Jay-rp8sy
    @Jay-rp8sy9 ай бұрын

    Thank you for the video. I have a question, what do we do when q doesn't equal + -1?

  • @zplusacademy5718
    @zplusacademy57182 жыл бұрын

    Extremely beautiful effort and execution sir ❤️🙏❤️❤️🙏❤️❤️🙏🙏🙏

  • @user-nu7zi3oi3w
    @user-nu7zi3oi3w5 ай бұрын

    I just appreciate you for your best teaching it

  • @gabrielleparalejas9510
    @gabrielleparalejas95103 жыл бұрын

    This some good stuff right here, can do a lot better than my current teacher.

  • @That_One_Guy...
    @That_One_Guy...5 жыл бұрын

    is there another way beside plugging in to find one of the zeros ? of course for polynomial above degree of two i know that there's also factoring (that would be hard though), but im asking for something new to find the zeros

  • @winterberry3412

    @winterberry3412

    5 жыл бұрын

    I know right?

  • @cricticalthinking4098

    @cricticalthinking4098

    4 жыл бұрын

    Learn how to use a graphing calculator, graph the function, then look for the x-intercepts.

  • @ULTIMARAGNAR0K
    @ULTIMARAGNAR0K2 жыл бұрын

    Won’t finding the roots in the last equation require you to use complex numbers to find the other 2 roots?

  • @CheyenneBurkett
    @CheyenneBurkettАй бұрын

    Wht is the -5 constant not included on the top?

  • @SomeRandom_personInTheInternet
    @SomeRandom_personInTheInternet Жыл бұрын

    THANK YOU SO MUCH FOR MAKING MY LIFE WAY EASIER!!!!!