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Rational Root Theorem

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How to use the Rational Root Theorem to narrow down the possible rational roots of a polynomial. You can then test these values using synthetic division to see if they are roots of the polynomial.
0:10 What is the Rational Root Theorem p/q
0:58 List of the Possible Rational Roots
2:53 Synthetic Division to Test the Possible Rational Roots
4:32 Factoring to Find the Remaining Zeros
5:02 Writing the Polynomial in Factored Form
5:27 Graphing the Polynomial
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Опубликовано:

23 авг 2024

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Комментарии : 202

@TozkahsKorner8281 2 года назад

the fact that a 6 minute video that is half a decade old was more efficient and enjoyable then my teacher's 2 hour lecture is wild

@arzan6871 Год назад

I honestly agree, my teacher spent about an hour explaining this and the factor theorem, and he explains it in 6 minutes is just wild. thank you so much

@EmpoIeon Год назад

2016 was not that long ago :/

@mbrachi4933 Год назад

@@EmpoIeon its 7 years ago

@DeeDee_Nola Год назад

@@EmpoIeon kind of was relatively

@joeshmoe8062 3 месяца назад

and I'm still using it which is crazy

@connorsucksatgames2263 3 года назад

This is incredibly useful even 5 years later. Thanks Mario.

@EmpoIeon 2 года назад

You're welcome

@nickcrowe9862 6 лет назад

good shit thanks mario

@camcamcamcamcamcamcamcamcam 4 года назад

your welcome

@arav4045 3 года назад

bruh funniest comment here lmao, nick acting like mario his homie or he know him irl lmaoo

@saketmurali4985 3 года назад

@@arav4045 he does, he's his son 💀💀

@arav4045 3 года назад

@@saketmurali4985 damn

@saketmurali4985 3 года назад

@@arav4045 just kidding

@nesyboi9421 2 года назад

My teacher was gone and assigned Edgenuity work while the sub was in, and the sub had no idea how to help and Edgenuity's videos overcomplicate things, so I came here and bam! Makes sense now. You will not believe how many math videos overcomplicate things nowadays, thank you for being clear and simple, you really helped me and my classmates out a bunch! thank you so much!

@aidandonaldson7 2 года назад

This was a very educational video. I like how you get specific about all the details and explain any knowledge needed before the next idea. Well done!

@KrakenDoesEverything 5 лет назад

damn you're fast at solving, you deserve more subscribers sir

@MariosMathTutoring 5 лет назад

Glad you are benefitting from my videos and channel Serge!

@yaakcon 2 года назад

You are an incredible human being. Thank you so much for explaining this so easily. My son, who is 13 years old, is taking Algebra 2 in 8th grade. He is so smart but he is sometimes lazy and he does not like to do his research to learn. I have been helping him find videos which are not confusing and can get to the point.

@stellagyan8200 2 года назад

Is it normal for schools in the US to teach students in 8th grade this topic?

@yaakcon 2 года назад

@@stellagyan8200 It depends. Not all of them but some schools place some students in a higher level math class.

@stellagyan8200 2 года назад

@@yaakcon that's interesting gd to know

@amog316 7 месяцев назад

I don’t know about other schools but I am a Junior in highschool and am taking Algebra 2

@Lyecrenn 3 года назад

wow, i just learned this from my teacher, didn't understand. bam i now know how

@Voice_Ai Год назад

Ive looked at a lot of rational root theorm videos but this one is the best. Subscribed immediatly

@shargor 2 года назад

This is one of my most favorite videos on RU-vid. No BS.

@HanaManesh Год назад

Thank you so much! This is exactly what I was looking for and asked about in your new video's comments.👍

@MariosMathTutoring Год назад

Great!

@syldris 2 года назад

Totally forgot this that I learned it in Algebra 2, and now I came here to factor Characteristic Equations of Recurrence Relations for Discrete Structures course... Thank you! It helped a lot!

@76wykes 7 лет назад

You explained it very well! Your videos are quite helpful.

@MariosMathTutoring 7 лет назад

+Vincent Tye awesome! Glad you are finding my videos helpful!

@eliteturtle6090 3 года назад

Im kinda relying on you to have the right video now that im on zoom and not paying attention in class, so thanks, and keep making more vids plz.

@aliceemerson2487 2 года назад

You're an angel and a very good teacher, I appreciate you so much. I hope you're doing well.

@barrymacogner4493 3 года назад

Possibly just saved my quiz score

@tweetiebirdgaming2113 4 года назад

Your better than my Teacher in Algebra😂co'z i can't understand when he's teaching to us

@MariosMathTutoring 4 года назад

Glad you like my teaching!

@elostroymauricnerbieran2594 3 года назад

The moment you gave me how to find P and q, I instantly know what the hell I should do. Our book was so untouched towards their audience, like come on man, show and tell! Not tell and tell, give us some arrows. I don't want to sound like a boomer but back in the day, they at least have some kind of clear directions.

@stevewest6133 4 месяца назад

Thanks Mario! Just one tip to add... You can factor out 2 from the original function and that will reduce the possible number of roots and get rid of the fractions :) .

@jeshwanthpalakonda4716 2 года назад

wow, this was way easier to understand than the lesson I read!!! Thanks so much😃

@mftuitioncenter Год назад

A 7 year old video has made me understand the concept , unlike the 2 hour lecture that the lecturer explained this

@lyricharper357 Год назад

this 7 year old youtube video did in 5 minutes what my teacher couldn’t do in 3 weeks, i love school.

@Giankurl 6 месяцев назад

this is a very informative and use full tutorial of the rational root theorem, thank you sir

@MariosMathTutoring 6 месяцев назад

Glad it was helpful!

@glenmballonjr368 Год назад

i had trouble factoring for some reason and my school would not explain it, this helped a lot

@erikm6515 10 месяцев назад

Bro ended my crusade of 2hrs trying to understand this thanky you so much 😭

@angelikcakes8814 Год назад

thank you so muchhhh i love the explaination you gave rather than me just blindly following steps

@ethanshao7002 Год назад

Thank you for your Rational Root Theroem Video. It helped me understand how to solve the problems that I had trouble with.

@MariosMathTutoring Год назад

You're welcome!

@jayden7194 9 месяцев назад

I love how you teach to the point. thank you

@MariosMathTutoring 9 месяцев назад

You're very welcome!

@Omar_A_Mosaad Год назад

That was very helpful man Thanks for the amazing simple explanation ❤️

@noneother1481 5 лет назад

Saved my grade in Algebra II, thanks a ton

@MariosMathTutoring 5 лет назад

You’re welcome! Glad my video helped you!

@melaniegonzalez8316 9 месяцев назад

my college professor made this seem impossible, but i get it now. thank you 🙏

@JoshuaClingman 3 года назад

You make it so easy to understand! Thank you!

@ten8347 Год назад

How did you get (x-3)(x-2) as the factors? I don’t really understand that part. Could someone help explain that to me?

@Omar_A_Mosaad Год назад

It's a quadratic equation x^2 - 5x + 6 So the -3 and -2 came from that their sum is -5 (the second cooffecient) and their product is 6 (the third cooffecient)

@ten8347 Год назад

@@Omar_A_Mosaad thank you 🙏

@akashayaqub7175 4 года назад

This video is a great resource. One question...If I have many possible solutions, but I find one of them, do I still have to test the remaining solutions or could I stay with the one I found? Thank you for all that you do!

@clipcity707 3 месяца назад

5% of my class time, is all it took for you to teach this

@ddjdj3034 5 лет назад

Is there an Irrational/Complex Root Theorem? Or something of that nature? Because it sure would suck to try and divide every single combination and end up realizing that all the roots are irrational or complex so you still don't know how to factor the polynomial...

@reignbeaxtr7767 7 месяцев назад

this video has taught me a lot, thanks for this

@MariosMathTutoring 7 месяцев назад

Glad to hear it!

@chase5015 Год назад

Thank you im reviewing for my midterms.

@Left4Sharkbait 3 года назад

Understand a lot better now! Before just couldn't understand or retain info from teacher

@trojanhorse7282 10 месяцев назад

taught me what my teacher couldn't in 6 minutes

@takumifujiwara5737 2 года назад

ur the best maths teacher

@mathivanan4517 3 года назад

your'e a good teacher

@user-gp2sf7kx2g 7 месяцев назад

I realized that rational root theorem was easy to understand after i watched this video

@parvsheth5078 3 года назад

Just a doubt, can we first cancel out the 2 from all the terms? It would make it easier

@chrrsy 3 года назад

yeah you can he said so in an earlier comment :)

@nicksiebel4668 3 года назад

what a legend you are

@paulwin9036 4 года назад

Is there a specific reason to use synthetic division rather than just replacing x with the rational roots?

@MariosMathTutoring 4 года назад

Paul, it is just usually quicker that’s all.

@unmask1o123 3 года назад

This is really helpful thanks👍! now I can finally start my math homework ;-; hope all of you are the same XD

@flyingl1393 3 года назад

LOL yes

@blackoutcurtains1 Год назад

this video saved my education you don’t even know

@davidparks4835 Год назад

My teacher needs to give their paycheck to you

@owensmith6571 2 года назад

learned more in 5 minutes than 5 hours with my teacher

@morgantaylor06 Год назад

Great explanation, thank you!!

@motherof3pearls 4 года назад

This was a really fun 4th degree polynomial problem to work. But my son Math Prof seems to seek out even more exotic problems such as the one here: (4x^2-3)^2 + 7(4x^2-3) +10 = 0. After factoring and simplifying we notice that it is a 4th degree polynomial as well and should have four solutions. How should we go about such a problem? U-substitution or synthetic division? Your help is most kindly appreciated. 🥴 Thank you!!

@MariosMathTutoring 4 года назад

Sheryl I recommend doing a u substitution for 4x^2-3

@MariosMathTutoring 4 года назад

Then factor from there and set the factors to zero to find the zeros.

@lindak8589 7 лет назад

Nice explaination, thanks

@MariosMathTutoring 7 лет назад

+Linda K thanks...glad it helped you.

@juanbecerril374 6 лет назад

Notification squad 💪🏿

@alfredosalgado4174 4 года назад

I love your videos Mario!!! Always great but you did forget the y - intercept at Neg. 12 :)

@robby-_-001 3 года назад

Thank you all the way into 2021

@irupachauhan7905 5 лет назад

I understood everything. Thanks a lot

@MariosMathTutoring 5 лет назад

Awesome! Glad my video helped you Irupa!

@irupachauhan7905 5 лет назад

@@MariosMathTutoring Thanks

@nerdycloudproductions 2 года назад

It’s funny just how many of us just have terrible teachers and are coming here for information LOL

@paulmaggiar8274 Год назад

Thank you Mario. Wouldn't this example have been much more manageable had we factored out a 2 from the outset?

@gagarine42 6 лет назад

Thanks. Very well done.

@MariosMathTutoring 6 лет назад

Your welcome! Glad you liked the video!

@buckyrx7 6 месяцев назад

How do you know which numbers to try for synthetic division after using the Rational Root Theorem? Is it just trial and error? That can be time consuming especially if you have a polynomial with a large constant having a ton of factors.

@sethkim2949 5 лет назад

Thanks Teacher Mario this helped me a lot!

@MariosMathTutoring 5 лет назад

Glad my video helped you!

@karangupta7793 6 лет назад

Can I find question on rational root theorem in my SAT subject test math🤔🤔 I didn't find any question on rational root in any of the sample paper I tried🤔🤔🤔🤔

@denisetion5584 Год назад

Hi. In the 2nd example of synthetic division where we use 1, why is the 2nd number not -12? Thanks

@justinraynor4983 6 лет назад

thanks it really helps

@MariosMathTutoring 6 лет назад

Your welcome!

@Roccoutlukx 8 месяцев назад

Why can’t people like this be my teacher 😢

@aleaiactaest6503 2 года назад

Probably the most tedious math topic so far

@neilkaul2449 3 года назад

Wow this was amazing thank you!

@daiiruss2037 7 месяцев назад

Hello sir can you tell me how did it become 2(x²-5+6)? did u somehow divide it by 2?4:33

@sorellana2154 2 года назад

this rocks, man! thanks!

@violettiourestinpeacetechn4742 2 года назад

Why does the synthetic division test the answers out? Couldn't you just insert the values as x to see if it comes out as zero?

@strike2091 Год назад

thank you iw as stuck on calc hw no longer

@MariosMathTutoring Год назад

You’re welcome!

@micadaga3473 9 месяцев назад

just a question, the number of degree/exponents hints how many zeros we have to find, correct? what if the highest degree of exponent is only 1? do we only have to do the substitution part because we are only looking for one zero? Thank you so much in advance! 💕

@MariosMathTutoring 9 месяцев назад

Yes the degree tells you the number of zeros including complex zeros, imaginary zeros, real zeros, and multiplicities.

@micadaga3473 9 месяцев назад

@@MariosMathTutoring So if the highest degree is 1, do we only have to do the substitution part because we are looking for only one zero?

@amanda-rs6bm 2 года назад

Thank you for this!

@klingbeil7281 4 года назад

thank you, good video, easy to understand

@MariosMathTutoring 4 года назад

You’re welcome!

@fortimusprime 4 года назад

Excellent video tutorial!

@MariosMathTutoring 4 года назад

Thanks!

@fortimusprime 4 года назад

Mario's Math Tutoring You’re welcome! You explained this in less than 10 minutes and helped me pass a Pre-Calculus test!!! Keep up the great work!

@MariosMathTutoring 4 года назад

Glad my video helped you!

@markopp7873 4 года назад

What if there is no constant? Does "p" become the last coefficient? It must...........??

@mirzabaig3520 4 года назад

I believe you would take out x first

@joeyenniss9099 2 года назад

Thank You!

@stevenphan4453 2 года назад

@cinema187 4 года назад

signed in just to upvote

@mekdestsegaye9825 2 года назад

Very helpful thanks

@brandonsvideos123 3 года назад

very helpful, thanks

@PeggieWeader 2 месяца назад

This is beautiful. However, he could have made this much simpler by dividing every term by 2 before he started.

@lavishkumar9075 3 года назад

Very helpful video

@once_sharrron 2 года назад

Thank you~

@hanmelol7073 Год назад

Thanks Alottt!!!!

@timacorn2536 5 лет назад

mr. mario do u have to do synthetic division or can you plug each possible root into the original function?

@MariosMathTutoring 5 лет назад

You could plug each value in to the function and see if it equals zero...the synthetic division is just a quicker way of doing the same thing....hope that helps Tim!