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

[@TheOrganicChemistryTutor]

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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

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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.

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Mmmmm that's amazing, in 10 seconds

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@@notsofiasco3 years later?

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[@honeyortiz1005]

Thank you SO much. At first I thought you had to plug in every single factor to find all zeros but then I realized from your video that I only had to find one zero from plugging in and then use that zero and the quadratic you get from synthetic division to find the rest of the zeros. I have a test tomorrow and this made me feel so much better, again thank you so much please never stop making these videos.

[@tylerdruskoff9689]

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

[@arc1671]

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

[@jacebrowy1420]

Agreed but it still helps

[@LeytonVelardi]

yea i'm in the comments looking for how to do it if the first term isn't 1

[@chair1694]

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

[@ToBreatheMusic]

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!

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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!

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Goodluck man!

[@sogeqt9188]

just wanted to say that this is an Algebra 2 concept

[@chekzz5352]

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

[@Manny24_8]

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

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

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

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

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honestly same

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

[@1nonlytorres757]

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

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

[@stickshiftstarship]

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

[@lolerishype]

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

[@willw4096]

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."

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[@georgesadler7830]

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.

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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 😊

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[@Justaguy-p2h]

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.

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As a dude whos knowledge at math is Mid-Average,You have no Idea how much I want to thank you from the bottom of my heart for this lesson

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any one else's teacher showed them the long division route then the quadratic formula ? I was so confused , so grateful I came across this video !

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

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kzbin.info/www/bejne/jWqyc6StZ69_pqc this video explains it

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Find factors seperately

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I tried to read this from my textbook and that was an awful experience. Watching this video helped to save my time

[@anastasnikolov9396]

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 :)

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

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How did you get the 3 in the first equation

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Oh my goshh. I still don’t understand and I don’t know what I’m doing wrong. You said if it doesn’t equal zero there’s a problem. What’s the problem!? I don’t know what I did!!!

[@cassandrafitydjx7462]

Remember factor theorem? If the polynomial is factor to the division, it should result into 0, if there is a remainder, then it is not a factor.

[@lexus7154]

what if the leading coefficient is > 1?

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for real

[@johnmeinert6600]

p/q applies to all factors of p and q, so for example if the factors of p are 1, 2, 3, and 6, and the factors of q are 1, 2, and 4, then the possible roots are all the combinations of +/- p/q, so in this case: +/- ( 1/1, 1/2, 1/4, 2/1, 2/2, 2/4, 3/1, 3/2, 3/4, 6/1, 6/2, 6/4 ), and then when you take out fractions that equal the same thing it's just +/- ( 1, 1/2, 1/4, 2, 3, 3/2, 3/4, and 6 ). hope this helps!

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

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