Rational Roots Test / Theorem

[@arav4045]

I was three year olds when this video was made. Now this same video is helping me 11 years later

[@redumptious2544]

Damn bro. You lookin into this by the age of 14 🤙

[@arav4045]

@@redumptious2544 fr

[@eR1ck_11]

Same bruhhh😬

[@chukwujekwuanazodo3129]

same here

[@tomatrix7525]

@@redumptious2544 in Ireland we do this at 12

[@pizzafreak1175]

I swear! This man saved me from going insane and failing my Algebra 2 class during the summer! The teacher was so awful. Thank you!

[@CloudDinoGod]

this is such a basic topic

[@mariaangelikagongona8603]

yabang

[@nps3bbsy329]

ya rema

[@tumimbanghymarvannd.8603]

Angel Gongona oo nga po😂

[@martinmoraleta7802]

Same here, my pre calc professor sucks. This guy is saving my ass from failing.

[@aryashivakumar]

at 4:12 you said "you get negative five" but the numbers are 2 and -3, so 2-3-11+6=-6, still not zero, but just clarifying in case anyone else caught that

[@troydelantar7899]

I have also noticed that, because 2 - 3 is equal to -1.

[@UnbreakingSOUL]

I NOTICED THAT OMG I JUST SAW THIS COMMENT, weird is that I also put 4:12 👽 very timing

[@UnbreakingSOUL]

@@troydelantar7899 maybe its just a mis-understanding

[@momo-debest]

he also made a mistake at 5:12

[@jvaniee]

Use the rational roots test and then plug the possible roots back in the polynomial to see if they = 0. Or, like what your professor did use the possible roots and the polynomial in synthetic division. If the remainder is 0 then it's a root. Both ways work but it'll probably be faster to do synthetic division.

[@nespecialistin7676]

Man, you explain math better than all of the math teachers that I used here in Bulgaria. Thanks bro!

[@patrickjmt]

if you are using real numbers, one can not just look at the degree and conclude the polynomial has that many roots. consider f(x) = x^2 + 4 this has no roots (again, using real numbers). the degree is the maximum possible number of real roots. euler (i think) proved that there will be n solutions (some repeated) to a n degree polynomial if we use complex numbers - it was his phd thesis!

[@thelasagneman6184]

goes through 12 years of math, never hears of this, hears it, is ever so grateful, you sir are a legend!

[@assassinblackop]

You're doing God's work.

[@_A_343]

lol

[@markianvulcan9479]

LOLL

[@ahsanulhaq8056]

Foolish!! No one is like God in any context.

[@agentr0077]

@@ahsanulhaq8056 🧒 CHILD 👶

[@stormzsamurai]

This video is helpin saving my grade in alg 2 rn. Thank you so damn much man. I have no idea when this came out but im so happy this is here!!

[@aadidesai1340]

5:31 54-27=-27 -27-33=-6 -6+6=0 Nice for you to help us, but please recheck work. + for the effort

[@sirruffalot]

Patrick...I love you.. I've been watching your videos for quite some time now, you helped me through algebra, stats, precalc, calc etc..

[@Mahmzo]

It seriously annoys me how I learn concepts in under 3 mins on this channel 😂😂

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! Also, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly :)

[@vetacoth]

You are the best math teacher on KZbin. Without you, I would have failed so many classes but I have to ask, when will this ever be applied to life?

[@patrickjmt]

yep! i hope it made sense for you : )

[@tanggapandaniela8342]

Correct me if Im wrong, isn't it 2-3-11+6=-6?? Not 10? From the first equation u gave.

[@jelly6023]

I was thinking that only I noticed it, made me do a double-take

[@charlieliu7719]

Same

[@nInOwarrior0312]

Unless one of them is suppose to be positive/negative, also remember PEMDAS

[@Maryz0lSunny]

Yeah it's -6

[@gabriel922987]

U right fam

[@andreadelossantos164]

I think it's not -27-33+6 it should be 27-33+6. Just get rid of the negative sign in 27 .

[@promastrouvant3002]

Andrea Delos Santos thats -27+-33

[@charlieji8781]

u r rite

[@patrickdeveloper7186]

@promas this is misleading information and people will get confused, please correct it. Or further explain it.

[@zorenmaniego5698]

@@patrickdeveloper7186 at 5:30, The guy subtract 54 and 27 in the '54-27-33+6'. 54-27 is positive 27, not negative 27. That's why the 27 in his -27-33+6 should be positive. But since he did calculated the 27 as positive despite it visually doesn't, he answered the equation correctly.

[@slysal5]

54-27= -27 ?????????????

[@patrickjmt]

yes, first factor out the x. then you can use rational roots thm on the polynomial of degree 6

[@haiderkazmi8806]

i was 12 years old when you uploaded this video and now i am 26

[@NeatherBen221]

This guy saved me from failing my Algebra 2 class during this year! The way the Connexus program is so sketchy! Thank you so much!!!

[@thinkfree5008]

I have my test in less than 1hr and from the bottom of my heart thank you so much.

[@patrickjmt]

good luck!

[@Coughi3]

I think at 6:41 , if you expand the bottom function, it doesn't equal the top function. Instead it equals the top function / 2. If you replace (x - 1/2) with (2x - 1) then it works. :) . . . . . ya

[@miker3701]

Studying day before major assessment. This is the best vid I found after an hour of looking. Thanks man

[@samsteve9220]

Exactly what I was looking for

[@patrickjmt]

@Zen113 what i am doing on youtube is more effective than what i could do in any class room i think.

[@DraoJasra]

Thank you, so much. Your videos help me with math more than any teacher I've ever had

[@projux5778]

You sir, are the reason I will pass my math quiz tomorrow.

[@weiyuan20]

well did you pass?

[@sureshotshorts1207]

U asking after 3 years

[@JuanReyes-rs6em]

@@sureshotshorts1207 sometimes ya just wanna know

[@Robert-ur5xy]

Did you pass?

[@patrickjmt]

glad to help!

[@ShrimpWizard]

You saved my Math grade ,Sir!! Thank you so much for such an awesome video!!

[@patrickjmt]

i have a video on synthetic division if that helps : )

[@manshagoel]

Do you have one for integer root test/theorem

[@athenstube]

You are really helping me along the path to my math degree. Thanks Patrick!

[@dsps301]

I wanna take a minute to thank you, for spending time to help me, and everyone else who has seen your videos! Keep making them! :D

[@Kapil65984]

Superb i am watching it after 11 year

[@chloecox7715]

Your videos are a blessing for me during this covid 19 crisis. THANK YOU!!!

[@UtuberKARAM]

OMG you made my life so much easier i have a test in 3 hours... i was gna FAIL thank you thank you thank you keep up the great work :D

[@chinmayvaishampayan7133]

Are u alive?

[@felxsvoice1848]

Just found your videos thru my college algebra class. You're so much more help than my teacher herself...

[@patrickjmt]

glad i could help you :)

[@Adriennee99]

Thank you it made things a lot clearer and connected everything I learned so far

[@meredithcamper3192]

At time -1.23 you note that 57-27=-27 and then go on the day that -27-33=-6, just thought I would note that 57-27 is in fact positive 27. Thank for making this video though!

[@rithvik]

Not trying to say Patrick's teaching skills are any less, but part of the supplement to his teach skills is the ability to rewatch and pause his videos to learn at your own pace. This is an added bonus to his skill to easily explain math without using words that are superfluous, as most math theorems do. Thanks so much for helping me out, been watching since 7th grade Alg 1, now am a freshman in Precalc :)

[@davidhuang5645]

Best math teacher on KZbin.

[@eternalbane996]

Thanks!

[@cryomancer20]

I was overthinking this cause the other videos made it feel complicated. Thanks for explaining it straight on :)

[@konopong]

Just to mention, after you have determined the three roots, when you write f(x) you need to include a multiplicative constant factor, which turns out to equal 2. That will give you the function you started with. Another way to find the roots and factored form of f(x) is that once you have found one root you can divide (syn. div.) by that factor to determine the remaining quadratic, and then factor the quadratic.

[@anamikajha7210]

Drop a confident reply if you got me today after so many years ❤

[@WLOfails]

Thank you so much! I never knew how simple this type of problem could be and now I can start my homework... before school reopens tommorow...

[@born2race17]

Slight error: At 4:18, 2-3-11+6 = -6, not -10. Though it doesn't affect the outcome of the problem. ^_^

[@patrickjmt]

yes, i just need to remake this one later today! : )

[@fmalove2]

Thank you so much! I had a hard time with figuring out where the fractions came from, but now I know!

[@patrickjmt]

no, u can always just reorder it

[@gangleader.7x]

I was near 3 months old when this vid was made now it’s helping me after 14 years

[@Oaishe]

Thank you soo much for this video!! I was so lost but now I understand! Thank you!

[@xXwannabeguitaristXx]

I wish you were my math teacher. I mean, I understand everything I needed to understand by watching your short videos than being in a room for an hour and a half! :)

[@spinel-lipatashaneloreala.6200]

i wasnt ever bornn when this video was made.. then it helped me 13years later thank you

[@MarsTheProgrammer]

thank you so much sir, without you, i wouldn't pass calculus and therefore not be able to get into computer systems classes in college.

[@azmoto-in5116]

Thank you very much you are a very pro efficient teacher!

[@patrickjmt]

@aceonx not necessarily real, there can be complex roots as well

[@jackjik5076]

You helped me get an A in this chapter, thanks.

[@ClaireDianneRamos-rw2wu]

I was exactly 4 months old when this video was made. And now I'm 15 years old and this video helps me.

[@cynthiajones5116]

This video helped me explain this concept to my high school students.

[@manyasuhag67]

for some reason my math class books and other material teaches weirdly and complicates stuff. This was very helpful!

[@Neighthann]

bro you rock i learn more math on you tube than in class somtimes

[@ШерозАлижанов]

dude, thank you very much, next month I will have an entrance exam in mathematics at the Lyceum, and this video helped me understand the topic, thanks)))

[@patrickjmt]

@xXwannabeguitaristXx well, not really, if it was not a constant, you would have a power of x, which you would factor out. then you would be left with a constant (assuming the powers are in descending order) and you would proceed from there. make up your own example to see what i mean.

[@WestSTL]

its almost 1 a.m. and I have a quiz tomorrow in honors alg 2 on this and I had no idea what was going on until this video. THANK YOU! you accomplished in 6 mins what my douche teacher couldn't in 90 minutes

[@junqianchen7128]

you are much better than my math teacher!! thanks a lots!!

[@イエル-x9w]

thanks so much for the solution :) I was having a hard time using synthetic division. I'll try doing how he's doing.

[@trishiasarmiento374]

THANK YOU

[@ryanholmes5294]

You are a life saver for my algebra 2 final!

[@Jaxamuss]

I'm sure it's not to important now but he should have used synthetic division to check. it's a lot faster. if you don't know what synthetic division is, look it up, it's very helpful for dividing polynomials

[@aneesak-ar-im3869]

JaxamussAwesomessMaximuss of course he could’ve used it but this is the rational root theorem that he’s trying to teach us (Yh I know this is like 2 years late oops)

[@Supunay]

@@aneesak-ar-im3869 no such thing as late on youtube bb

[@CrimsonKnightmare1]

Ive heard synthetic divion is very limited

[@mikuculus3720]

CrimsonKnightmare How so?

[@backpacker_mac]

Awesome! I am sick and I am still learning the stuff my classmates are in class. Awesome!!

[@B.W.L.9786]

Video is 11 years old but still better then my math teacher thanks man!

[@patrickjmt]

you are welcome!

[@XgtkidX]

thanks so much. helped me tons with my finals!

[@chinmayvaishampayan7133]

Are u alive????

[@iexoticcraft]

u still alive bruh?

[@erinrisinger2413]

Why are you not my teacher, you make it so simple and easy to understand.

[@julianalinares9825]

thank youuu ! you simplify things so muchh

[@yougotnojams5182]

thank you so much,sir! You're much better than my math book !

[@patrickjmt]

Happy to help

[@RidinMusicLines]

@aceonx the amount of roots depends on the highest power x factor... so in x^3 + x^2 + x + 4 or something, 3 is the amount of roots, because this is the highest power x factor

[@negosyante123]

Be careful when you are adding or subtracting negative signs. It's actually not -27 but +27-33+6 =0

[@StormForthcoming]

ohhhh thats why i was confused lol

[@negosyante123]

@@StormForthcoming yeah, you can visit my profile as well but I don't think so if you can understand because I used Filipino language.

[@_A_343]

This video helped a great deal. Thanks you.

[@patrickjmt]

@sarazuu yep, somewhere

[@senchi0kodo]

very helpful, thank you!

[@mehran528]

I was 1 year old when this video was made and now 14years later this video is helping me😀😀

[@unfaithful1034]

You explained a lot better than my package of notes. Thanks!

[@nps3bbsy329]

ufufu

[@iankelley9302]

I'm in algebra three and we never were taught this.

[@liyan2168]

My Maths teacher sucks at an epic level... Thank u!!! I understood now

[@maylamalacura1523]

Thank you...

[@michaely5375]

Thank you so much and God bless you. The best math teacher.

[@yourvideosaregomi899]

U put negative 27 even though it's positive

[@khomchat1]

Nope - 3(3)`2 is 27 since 3*3=9 and 9*-3=-27

[@EstiagoGaming]

@@khomchat1 he is taling about 54-27 =27 not -27

[@khomchat1]

Oops looking at the wrong one

[@edmundsin4862]

Yes, he wrong -27 but he still computed it as positive 27. So no actual error that affected the answer.

[@mr.lemonjuice9098]

But the answer still is correct

[@herniethetwig7994]

Thanks for teaching me what my teacher didn’t

[@夜雨声醒]

My teacher really confuses me, now I understand thank you.

[@theecreativesoul]

Thanks! My teacher taught this in a terrible way. You are so much help.

[@patrickjmt]

thanks!!!!

[@janellehafalla3659]

this literally saved my life

[@predatorzealot1000]

didnt know it was uploaded in 2008 but thank you so much for uploading this video it really helped a lot

[@wayofwonderer5929]

All your videos Such a valuable gift 🎁 for me on youtube .

[@raikantopeni9532]

You made this very easy. Thanks

[@MathMikie]

i like that can that solve for powers say 4 or 5

[@centrax4716]

thanks man you explained it really well

[@ArminGr]

Simply done! Thank you !

[@colinabcdefbelen2455]

thank you☺

[@francisr8205]

Shouldnt you consider the negative versions of the possible rational roots too?

[@gabbyjay8581]

this is a really lengthy process, but it’s the only thing i understand so thank you :))

[@patrickjmt]

@xXwannabeguitaristXx factor out x^2, then just do what i do in the video on the remaining stuff