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
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
4 ай бұрын
I enjoy your lecture
This guy is saving millions of students from failing. godbless this dude!
@rutii.a6428
2 жыл бұрын
Amen! He saved me too.
@roblominmus
2 жыл бұрын
I legit have a test on this topic tomorrow, he just saved my grades.
@absolute6422
2 жыл бұрын
He’s a literal god send
@mekdestsegaye9825
2 жыл бұрын
Amen
@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!
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
2 жыл бұрын
well, this is wholesome
@UNKNOWN-bp8it
2 жыл бұрын
@@JW-oi4mo Agreed.
@al-khatabalshibli393
2 жыл бұрын
well thats cute
@nataliecampos5888
2 жыл бұрын
Bruh my brother yells at me.
@Zeshal_asmr
2 жыл бұрын
Nyc trick... 💜
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
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
4 ай бұрын
Mmmmm that's amazing, in 10 seconds
@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
There is a 100% chance that i will never use this for my nursing degree lol
@googlewebsite5953
3 жыл бұрын
prbly not but ive heard theres a surprising amount of math involved in nursing
@twomarinesandadunce1107
2 жыл бұрын
Hey, a fellow nursing major using this bs
@bopiiq8947
2 жыл бұрын
honestly same
@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
2 жыл бұрын
Lol I want to go into an artistic career and I feel the same way. 🤣
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
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
4 жыл бұрын
Lol, same for me
@Em022
Жыл бұрын
CC life in Seattle
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
3 жыл бұрын
Same. I was just about to give up. Thank god I found this😭
@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😭
should've done a problem that's first term was something other than a 1.
@jacebrowy1420
3 жыл бұрын
Agreed but it still helps
"make sure this is a zero, if not, something is wrong" that scared me bruv. lol
It’s 1am and a school night. This hw is due tomorrow. Thank you so much
World's best tutor
@Angeloyoutube835
4 жыл бұрын
Right. I’d rather have this guy as a teacher instead of my current one.
@velsiz6217
3 жыл бұрын
Seriously
@jeibi6483
3 жыл бұрын
Ikr, i feel like i owe this guy my life😳
@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
3 жыл бұрын
amen
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
6 жыл бұрын
Goodluck man!
@sogeqt9188
5 жыл бұрын
just wanted to say that this is an Algebra 2 concept
@chekzz5352
4 жыл бұрын
@@sogeqt9188 its present in cal, precalc, and sometimes in algebra 2
@Manny24_8
3 жыл бұрын
@@sogeqt9188 I didn’t have it in my algebra 2 course lmao
@randommonkey4900
Жыл бұрын
@@sogeqt9188 i never learnt it in alg2 just learning rn in precal
This is a pretty consistent way of factoring high degree polynomials, there's no weird algebra manipulations, and it's very repeatable
why do you always sound like you are kidnapped and forced to make tutorials great video nevertheless
@natckwan
5 жыл бұрын
so we can get high marks on our test
@manalibisht6865
4 жыл бұрын
do u want him to act like a clown or something
@sora_is_my_dad420
4 жыл бұрын
It factors the polynomials or else it gets the the hose again.
@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
4 жыл бұрын
unfunny, stop trying to be.
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!
This voice introduces peace to my brain
@Yummycinnamonroll
2 жыл бұрын
Istg
YOU ARE A MATH ANGEL!!!!
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
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.
You’re a good teacher!!! Your videos are helping me with my maths. Thanks a lot man!!
this is the best channel existing in the entire youtube, thank you so much
I've been watching for 2 years now and just wanna say thank you so much this is really helpful
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!
I love you sir...I was on the brink of tears before finding this. Bless you.
Definitely buying some merch after my final, you've saved me throughout my entire pre-calc class
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."
for the last two answers (the square ones) could you simplify them in any way or are they just written like that?
always look for your videos when I have a problem in math. you got the best math videos on the net
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!!!
My instructor had us list all factors and try synthetic division over and over, your way is so much simpler! Thank you!
@lolerishype
Жыл бұрын
I suppose that method is technically more straightforward; but Organchem’s method is indeed faster.
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.
God bless this man fr…some of our math teachers don’t teach and just give the work but now I am understanding it!!!
So happy to have this type of teacher, i always understand his lessons this 2020......
Idk how I appreciate this. you’re phenomenal
thanks so much, you did it much faster and easier than other tutorials
Thank you, your video helped me learn a section the professor skipped over but was still needed for the final
Thx for the saving my ass entire high school year
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
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 😊
I use your videos for linear algebra (eigen values / eigen vectors). Thank you so much!
Hi I just want to say your video toturials are amazing I easily get it
I can't tell you how much I love your videos. You have countlessly saved my life from failing
YOU'RE SERIOUSLY THE BEST TUTOR EVER
In fact, you are helping a lot of people. May God bless you.
Thank you so much, I've been struggling with this concept and you helped me tremendosly!
This video is far more helpful than my professor was. Thank you so much!
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
Жыл бұрын
kzread.info/dash/bejne/iW2DpNOwYq2yoKg.html this video explains it
@brysongummerus6481
Жыл бұрын
Find factors seperately
Thanks for the help man im in algebra II and this is really helping me
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!
Question about the first example, how did the -5x turns into ±3? (In the introducing example thingy)
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.
Thank you so very much. All your video lessons are great!. Thanks again!
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
U teach better then my teachers u talk at a pace I can understand u
Can you use the method used to find the first zero, to find the others?
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.
Learn a lot from your videos! Can you please make one with function table of fog gof fof etc.? Thanks!
I don’t need to use the descarte’s rule of signs right?
im taking my final exam today and I can proudly say you pulled me through this course every single week without fail
thank you. i had forgotten how to do this and it was a great refresher!
Thanks for the guide man, really need it. Wish me luck. Have an exam 2 hours from now.
Thank you for the handy videos, allow me to get better preparation in college algebra.
this is helping me out immensely, thank youuuuu 😭😭
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
This made my life so much easier!!!! Thank you so much 💗
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 :)
By far my favorite KZreadr!!!! Thank you !!!
Love you man. Best on KZread.
This is so very helpful.. thanks man
Thank you for teaching me what my teacher could not
this helped me so much! thank you!
I love you so much man, I can’t focus in class for some reason so you’re a saint to me
im on differentials and i needed a refresher, thnk u sm!
would it still work for degree 4 above or degree 2 and less?
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?
Question! do I need to do the synthetic division part or am I good with just the x = 1?
Excellent. Thank you very much. What do you use to write on screen please?
How did you get the 3 in the first equation
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.
hi i just wanna ask, can u still use the rational root theorem without a constant?
So what would you do if the leading coefficient isn't 1?
Thank you so much. I know what to do on my quiz now❤️❤️🤗
Thank you so much for this channel... Truly a lifesaver
Thank you very much! this video helped me a lot. God bless you!💙💙
What if q is like 4 and p is 3, would I just use the common factor of +- 1?
Thank you so much your vids all ways help
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.
10:58 what if my b is already negative? Does it transform to positive or does it stay negative
Yo, just askin, what if the constant term happened to be 1? Is it factorable if the mid coefficient is higher than 1?
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.
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
u explained it better than my professor thank u
Thank you for the video. I have a question, what do we do when q doesn't equal + -1?
Extremely beautiful effort and execution sir ❤️🙏❤️❤️🙏❤️❤️🙏🙏🙏
I just appreciate you for your best teaching it
This some good stuff right here, can do a lot better than my current teacher.
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
5 жыл бұрын
I know right?
@cricticalthinking4098
4 жыл бұрын
Learn how to use a graphing calculator, graph the function, then look for the x-intercepts.
Won’t finding the roots in the last equation require you to use complex numbers to find the other 2 roots?
Wht is the -5 constant not included on the top?
THANK YOU SO MUCH FOR MAKING MY LIFE WAY EASIER!!!!!