Finding all the Zeros of a Polynomial - Example 3

[x0Gamble0x]

can u help me with my homework? please

[mjohnsoncuber]

YEAAAAAAAAAHHHH I FEEL LIKKA BAWSS

[AhiskaRustem13]

10x a lot, this was sooo helpful

[engysamad1]

Excellent .Thanks a lot . You are master in math :)

[hangv001]

can you please come teach at my school? I begggggg you!!!!!! My teacher doesn't know how to teach. She spent 30 minutes just to explain how to find rational zero. Thank you so much!

[timothytcliu]

everything else has online sources, but hey what about math? this is brilliant. thanks!

[rabbifilms]

@patrickJMT Can't one just plug the function into a calculator, see where the lines intersect, and find the zeros that way? or anyowne..

[patrickJMT]

@rabbifilms well, if you are going to use a calculator, just use it to find the solutions. why even bother to graph.

[AliensHateUs]

@jeleeymay97 You could use Descartes Law of Signs to figure out how many zeros you will have, however DLS does not show you which specific possible factors are zeros, just how many zeros there could be.

[jeleemay97]

is there a way to tell all the zeros without plugging and chugging every possible rational zero? because on tests and quizzes, that is very time consuming :(

[patrickJMT]

@jeleemay97 yes, it is very time consuming. to find zeros of a polynomial is actually a deep and important concept.

[LindaW54]

You are a baller! i like that factoring when you had a coefficient "3" in front of you're x^(2) trial an error at a glance ;).. keep up the good work! This video taught me well

[CrazySaver123]

I have trouble when the leading coefficeint is higher than 1 and you get a fraction, such as 1/3. Do you divide this number?

[mindkilla123]

@CrazySaver123 You leave it as a fraction, sometimes it will simplify like say you have something like y=3x^3+4x-24. You will have 24/3 as well as 6/1 for factors with the rational theorem. In that case, duplicates cancel out.

[sikanzon]

that's really useful, thanks

[XxStr8paintballerXx]

College algebra final tomorrow you are my savior!!!!!!!!!!!

[999saleh999]

@XxStr8paintballerXx

Your test was 5 days ago .. I am now saw your comment .. Tell me what you did in your test .. I hope you got a good grade

[coolman6566]

I have x^4 + 6x^2 + 9. I need to find all zeroes. all the zeros i found were plus minus 1, 3, and 9. i tried all 6 of them and plugged them in, but none of them came out to equal zero

[patrickJMT]

@coolman6566 there are no zeros for that

[jackyng008]

@coolman6566

there are any real zero for that?

i find it is (x^2+3)^2

but (-3)^0.5 is not real number

[ande66]

@coolman6566

As said, there are no roots for it, but if you want to simplify it you could use substitution and put x^2=u, then you will have u^2+6u+9. Solve it, you'll get it simplifies to (u+3)(u+3). reverse the substitution gives: x^4+6x^2+9 = (x^2+3)^2

[Valerie81]

i love you. thank you thank you thank you!

[patrickJMT]

@Valerie81 you are very welcome :)

[sea1127]

Thank you so much. Have a test tomorrow was worried but now i think im good to go.

[MP5er123]

Thank god for this video, I was so confused during my lesson today and this just cleared everything up, thanks so much. :D

[Staggger]

you need to get paid more...

This goes WAY over my head...

[NumBaONeHaTeRz]

Are people doing this in actual Calculus class? Because i'm doing this in my

Pre-Calculus class..

[patrickJMT]

@NumBaONeHaTeRz you do use algebra in calculus, of course.

[systemsteven]

@NumBaONeHaTeRz I'm doing this in algebra 2...

[cantfindanotherme]

i love you

[meganlwx]

how do u choose which number to start synthetic division? what if there are 100 possible ration roots? is there a better way to choose a number to start?

[ImaFez]

so if u plug in 1, then ur factor will b negative? ur remainder is 0 so ur factor would b x-1 and vice versa?

[xxtoinspirexx]

Youre the best! THANK YOU.

[joker5266]

Great... studying for my CSET, haven't done math in 5 years, this is a great refresher! Thanks!

[sarazuu]

why do you divide each factor of 40 by each factor of 3?

[sarazuu]

to get the possible rational zeros, do you divide the factors of 40 by the factors of 3?

[bmwandcadillacftw]

i love you

[TheEnriquification]

Hey, you're a lefty! :D

[richardsun7]

10 hours before my Differential equations exam, not worried. I got my man Patrick teaching me this stuff.

[patrickJMT]

@richardsun7 ha : ) if it is a diff eq exam, i think you are watching the wrong videos!

[nathanmccolloch]

@patrickJMT this actually is used in differential equations

[999saleh999]

@patrickJMT look man . you're the best !!

for the first time in my all exams Iget full mark ..

Thank you from the depths of my heart

[mthasan94]

I don't understand why I'm in a pre-calculus class if I can actually learn through videos online. Thank you so much for such a comprehensive series of videos. You've made math, arguably my weakest trait, a subject I stand out in now!

[brittsyoutoob]

thanks, that was the best video explanation I've found on this!

[patrickJMT]

@brittsyoutoob perfect!

[iMUSiiCO]

how come my teachers is saying theres irational zeros? like 2- i √3 and 2+i √3

[patrickJMT]

@iMUSiiCO because there can be

[dnthinkdrink1]

awesome this really helped for my calc class since we have to find extremas

[MrFrankthetank0000]

So there is no way of finding the zeros or at least narrowing down the options? Is it really trial and error?

[patrickJMT]

@MrFrankthetank0000 this is narrowing it down

[havoc9227]

@MrFrankthetank0000 It isn't trial and error, or at least it doesn't have to be, if you have a graphing calculator, you can plug in the function, where the line meets the x-axis is a zero. If you want to find the exact zero, press 2nd key and calc. button, and select ZERO option and then you can find your zero like that.

[MrChuckisgod]

Oh my God

u are the best :)

[NickMxxre]

I think my teacher left all this out..

[TheOffline23]

love all your videos. You are so much better than my teacher.

[jazzmanjunior]

Patrick! I studied with your videos and got a 98% on my test!! Thank you!!!

[patrickJMT]

@jazzmanjunior that is very good! congrats ; )

[rp1106]

Thank u so much!! U r a math genius! This is becoming very clear thanks to u! And the factoring in your head is sweet! :)

[4BrownBrotha]

Thank you so much, I have a test tommorow and its been three weeks since the unit started and i have learned so much stuff about polynomials its insane. I used all your videos that I needed for review and I have an even better understanding! Thank you for the great explanations, great hand writing, and great videos. Keep up the good work :)

[TheRealDealio]

How did you factor the 3x^2-11x-20? Did you just do grouping in your head?

[kwongsoo]

you are the bomb!

[johncleepowers]

Seriously thank you.

[hexer10]

OMFG you're so good, I hope all teachers are like you. Sadly, all of them are nothing like you.

[Crossfeet606441]

The next time my math teacher says "......blah....blah......blah"­ and stuffs like that for 40 - 60 mins, my bedroom will become my classroom, and the book will be my laptop, the page of the lesson will be youtube, and you will be my teacher for just 10 - 20 mins.

[OpenTheTrollGate]

man, this video is more useful than the remainder theory and synthetic division video

[darkness1130]

06.27 .. 84-84=0! (factorial) is equals to 1... just kidding..thank you a lot btw :D

[terezacuriel]

This video was so helpful! Thank you for posting this video as it provided such a helpful guidance for me. Thank you, thank you and a million thank yous. Thank God for Math geniuses like you!

[kelvinng9616]

How can i find the factor faster?

In the exam, i don't have much time to test all the possible number :/

[chrispycritter2]

Great Thanks!!!

[noobrages]

what if i cant find a single zerio using that trial and error method :p

[dmoneycutie1995]

why isnt 10 a rational zero ???

[poorluck1103]

Perfect

[aaroncarterfan911]

nerd

[poorluck1103]

@aaroncarterfan911 because of nerds we have 3D TV's, PS3, Xbox360, Nintendo 3DS, Iphones, and Laptops! That means your comment was a compliment! :)

[aaroncarterfan911]

@poorluck1103 ur prolly a nerd. the only cool/not-gay thing is contact sports

[poorluck1103]

@aaroncarterfan911 I'm a nerd towards weight lifting. Come at me.

[Narutofan1Pedry]

what can i do to sub 999999999............. times to your channel?

[sarqRodriguez]

Hey thanks dude, i got half way but got stuck with your video i was able to do the rest.

[SwaggCreator]

I was given a worksheet but I have never heard of this before! So i am sorry but i am lost!

[spirituelconnexion]

thank you

[sufiyah13]

omg thankyou sooooo much. I'm finally understanding this stuff <=) thankyou!

[diorain]

i wish u use ur right hand

[patrickJMT]

@diorain i wish u not write stupid comments

[EMOTIONZ80]

@patrickJMT i love you,Patrick.! lmao!!!

[OpenTheTrollGate]

@patrickJMT lol

[MrChainsawmanic1]

@patrickJMT what are all of the rational zeros of this: x^4 - 49

[patrickJMT]

@MrChainsawmanic1 factor it (it is a difference of perfect squares) ; you should be able to factor it twice using the difference of perfect square formula! (that is the hint i give you!)

[karate17100]

@patrickJMT

What if there is no constant? Like: 2x^3 + 14x^2 + 24x

Btw, your videos are a great help. Keep it up!

[patrickJMT]

@karate17100 you just factor out the x (in this case) and the proceed to factor as in the video.

[lEBANESe0AYAh]

THANK YOU!!

[Sylvanas17]

thank you!!!!!!!!

[xOxPaRiS2xOx]

looong problem. but veery well explained

[MsMuneca19]

what would be the best strategy to choose our factors to check if there zeros? For example on a test? And in my case we can't use a graphing calculator..

[MsMuneca19]

what would be the best strategy to choose our factors to check if there zeros? For example on a test? And in my case we can't use a graphing calculator..

[gnarlymarly805]

10 is a possible zero but he forgot to write it down.

[Keirosuke]

Guys, a short cut to find the number that equals to zero without guessing is to write the equation on the graphing calculator and hit Graph button. The point where the lines hit zero is the number that is a zero.

[patrickJMT]

@Keirosuke looooooooooooooooooooooooooooo­oooooool

[apocSe7en]

@Keirosuke WOW! Short cut indeed. In fact we don't even need to use any of Patrick's videos! Hell, we just need graphing calculators. Thanks Keriosuke! Now perhaps you can explain to me how I can sneak one of these "graphing calculators" into the testing center without getting caught.

[soccerplayaswaggg]

gahhhhhhhhh thank you againnN!

[oxygenada2]

i did not understand this at all

[oxshilo]

i would fail math without you.

[amaam89]

Why isn't 10 a possible zero?

[blaker440]

Excellent!

[cowguy1244]

You saved me. Keep it up.

[sergateway]

i axtually understood it.

[immigrantinc]

Your a god! I love your videos they are helping me in University!

[Eremenatar]

omg you explain it soooo much better than my math teacher

[flynig1]

These video are a gift thank you!

[GarrettTheHung]

Honestly, thank you for the video.

[airfeek00]

i was wondering does anyone kno if its possible to take linear algebra and calculus 1 at the same time?

[flopski]

People who say factoring doesn't make you happy, just can't do it.

[StillAware]

Technically it would be easier to use a calculator and plug all those possible rational zeros into f(x) and see which gives us zeros. Obviously it'd be less fun though :p

[mducky6]

@StillAware When I took Algebra 2 I couldn't use a calculator.