How to Determine All of the Zeros of a Polynomial

Рет қаралды 520,891

11 жыл бұрын

👉 Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero.
To find the zeros of a polynomial that cannot be easily factored, we first equate the polynomial to 0. Next, we 'guess' one of the factors of the polynomial and then use synthetic division or long division to find other factor(s) the polynomial. After we have obtained the factors and have factored the polynomials, we can then use the zero-product property, quadratic formula or any other applicable property or formula to evaluate the factored polynomial and hence obtain the zeros of the polynomial.
👏SUBSCRIBE to my channel here: kzfaq.info...
❤️Support my channel by becoming a member: / @brianmclogan
🙋‍♂️Have questions? Ask here: forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: / mrbrianmclogan
Organized Videos:
✅Zeros of a Polynomial by Factoring
• Zeros of a Polynomial ...
✅Zeros and Multiplicity of Polynomials | Learn About
• Zeros and Multiplicity...
✅How to Find all of the Zeros by Sum and Difference of Two Cubes
• How to Find all of the...
✅How to Find all of the Zeros by Grouping
• How to Find all of the...
✅How to Find all of the Zeros in Factored Form
• How to Find all of the...
✅How to Find all of the Zeros by Factoring 5th Degree
• How to Find all of the...
✅How to Find all of the Zeros by Difference of Two Squares
• How to Find all of the...
✅How to Find all of the Zeros by Factoring 4th Degree
• How to Find all of the...
✅How to Find all of the Zeros of a 3rd Degree Polynomial
• How to Find all of the...
✅How to Find all of the Zeros Without Factoring
• How to Find all of the...
🗂️ Organized playlists by classes here: / mrbrianmclogan
🌐 My Website - www.freemathvideos.com
🎯Survive Math Class Checklist: Ten Steps to a Better Year: www.brianmclogan.com/email-ca...
Connect with me:
⚡️Facebook - / freemathvideos
⚡️Instagram - / brianmclogan
⚡️Twitter - / mrbrianmclogan
⚡️Linkedin - / brian-mclogan-16b43623
👨‍🏫 Current Courses on Udemy: www.udemy.com/user/brianmclog...
👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvideos.com/about-me/
#polynomials #brianmclogan

Пікірлер: 185

@danielkadji3497 5 жыл бұрын

imagine taking his math classes in high school, you'll be set for life

@aebious8886 4 жыл бұрын

dude you have no idea. Im in college and I still watch his vids

@iviake3241 3 жыл бұрын

@@aebious8886 😂

@Sparkle352 4 ай бұрын

Cupcake

@youngransom7768 3 жыл бұрын

This king taught me more in one video than what my teacher has in a week. Thank you, Mrs. Hamilton for shoving 5 standards down our throats in just two weeks, then making us take a multi-day test on everything, with none of the fundamental knowledge to even find all the zeroes.

@MathLab4u 3 жыл бұрын

math teachers cubics as well You might look at some examples kzfaq.info/get/bejne/n9iTjcJ-ltOXeWw.html

@KimboCo 5 жыл бұрын

This is Pre calculus?!?! Why the hecketh is this the only thing ive done in Algebra 2 Also thank you for being better than my teacher

@ScottNguyenRCAC 4 жыл бұрын

Calculus is better than this.

@greenapple6404 4 жыл бұрын

There is still review in Precalculus.

@dontworryboutmyname8934 4 жыл бұрын

I’m doing this in college Algebra 😂😂

@kaylaelliott9436 3 жыл бұрын

I did this in advanced stats

@xfire3778 3 жыл бұрын

Precalculus is algebra 2 lol

@SecondHandShaun 3 жыл бұрын

Was about to jump out a window and then I found this. This man makes me pass algebra 2.

@kai1969charger 3 жыл бұрын

learned more in three hours from him than in three months of my 110 class

@MathLab4u 3 жыл бұрын

math teachers cubics as well You might look at some examples kzfaq.info/get/bejne/n9iTjcJ-ltOXeWw.html

@enderbartnik3148 5 жыл бұрын

Personally, I've always loved math. That said, the majority of my classmates do not. I feel that if we had such an enthusiastic teacher, that would not be the case. Thank you for all of these videos, they're amazingly helpful and very informative!

@aryamazandarani6373 5 жыл бұрын

Yeah me too. Last year for alg 2 i had the worst teacher i have ever had in all of my years in school so i averaged a C+ when i would normally get high Bs or low As. she just wouldn't stay after school for help or supply us with the right information before test day. She would teach us 70% of it and have us learn the rest from the sections of the textbook that she never told us about

@yuljul6215 3 жыл бұрын

@@aryamazandarani6373 Damn that's tough. I had alg 2 last year as well and boy did I have a hard time adjusting to the way my teacher taught my class. However I'm grateful I was able to maintain an A and bring up my high B's throughout both semesters, (all thanks to mclogan and yaymath lmao) I'm so glad I've moved on to pre calc. I wish you and everyone else good luck! Hang in there!

@yuljul6215 3 жыл бұрын

@Ender I have always been fascinated by math too. From elementary to middle school, it had always been my favorite subject! Unfortunately, when high school started for me, I was overwhelmed by new teachers and all eight of my classes, especially algebra 2. Freshman year was kind of a mess 😬 My confidence in math dramatically decreased since then. I attend a rather competitive school so everyone around me is smart and many of them are the biggest of the brains which really messed up my mindset. Anyways I'm good now lol I wish the best of luck to anyone who read this!

@confusedpotato9337 3 жыл бұрын

oh dang so my teacher just decided to skip teaching the very important part of finding what numbers to test - I seriously thought he was just pulling numbers outta nowhere and me being stupid just tests every single number less than 100 for every problem,,, this explains why others outside of his class can get the homework done within an hour while me being an idiot takes at least 3. Thank you for freeing up my life again ;D

@ryanandrews7109 3 жыл бұрын

My teacher is absolutely awful, and I am so glad these videos exist. I would not be passing Pre Calc. without them.

@ke00si12 4 жыл бұрын

imagin being in his class my teacher could never the way the students arent afraid to talk out loud give there answers, its truly astonishing you are an amazing teacher

@HeloisaChalom 3 жыл бұрын

DUDE THANK U. i wouldn’t be passing online precalc without this man

@laura_jones 4 жыл бұрын

i'm developing such a crush on this man.

@dawgtora.sushii 4 жыл бұрын

i feel u

@yolandaayala2267 3 жыл бұрын

this video clarifies my understanding at a conceptual level. Thank you Mr. McLogan !

@phlsphr42 4 жыл бұрын

@2:07, what exactly are you counting here? How are you getting the numbers 3 and 1? EDIT: Nevermind. For anyone else wondering the answer to my question, I found what he was talking about in his other video, here: kzfaq.info/get/bejne/aN1hn7umspzUknU.html

@beak4996 4 жыл бұрын

thx i had the same question epic

@braedentrefethen5437 3 жыл бұрын

Wonderful, thank you so much

@papercrownworlds2725 3 жыл бұрын

a life saver! thank you!

@kurokos 3 жыл бұрын

I had the exact same question as well. my thanks and appreciation.

@yesimafantastayzen3744 3 жыл бұрын

I listen to this while answering the tests. Honestly I feel like my brain works a lot faster while I listen to lectures while studying

@alyssanguyen2417 5 жыл бұрын

Thank you so much for this. I'm learning this in my freshman (highschool) math class but my teacher is really smart but can't explain anything. Thanks a bunch! I finally understand it!

@arminsmajlagic2907 3 жыл бұрын

This is very helpful, i had problems with finding eigen-values of an system and simply was not good enough to find them zeros...

@kifu1268 6 жыл бұрын

Nothing Else than a fantastic video! Keep up the good work. The World needs more passionate teachers like u that can contribute break up the sad, common view of math these days...

@brianmclogan 6 жыл бұрын

appreciate it. I 100% agree

@axtas 5 жыл бұрын

My teacher couldn't teach me anything the entire semester. I watched this video for the first 5 min and I FINALLY GET IT. Thanks for nothing BECKY (my teacher)

@excorific7514 4 жыл бұрын

How's Becky doing?

@may-bees 4 жыл бұрын

how do you know to choose 1 and 2 and not 5 and 10? or can you use whichever zero you want? i noticed the whole try each one but when there's too many to chose from isn't there a shortcut?

@shhh9162 9 жыл бұрын

thank you!

@belladonnaexperiment8301 3 жыл бұрын

Thank you! I'm at home for school for math right now your videos have helped a lot

@vahmed2420 6 жыл бұрын

Like legit .. thank you soooo much.. i was struggling in that the whole term 😭😭😭

@brianmclogan 6 жыл бұрын

you are very welcome! happy to help

@brandonb9416 5 жыл бұрын

Just what I needed.

@brileykick1598 3 жыл бұрын

My teacher goes about this fast and I love it and he has us do a ton of optional practice problems to hone it in but there are two girls in class who hold us back by twenty ish minutes almost every day because they have so many questions. I wish we could just move to a different class

@rfarrelldic 4 жыл бұрын

This is great... really well done and I congratulate you. But since there are only three answers and four possible answers, would'nt it be easier to just try out +1, then +2 right in the equation...... it turns out that plus 1 is NOT a zero , so therefore the other factors are what we are looking for.....

@Sultan_A 4 ай бұрын

Very Good, Brian McLogan

@user-oq1fy5fc8w 5 жыл бұрын

simple and genial thanks.

@georgesadler7830 2 жыл бұрын

Thank you for this beautiful mathematical video.

@iczy1794 4 жыл бұрын

it is the end of the year and i completely forgot how to do cubic functions, so i searched up how to solve and i start watching this video and it has the exact question that is on my assignment.

@SporteeGamer 2 жыл бұрын

If we plugin one by one factor in equation so that any factor equal zero so then we can get other zeros using synthetic division method. Remainder, equation and then factor of that equation or by using quadratic equation is it🤔🤔🤔

@farzinamatubbar1564 5 жыл бұрын

6:55 what is this method you used ? and what for ?(from UK we might use different methods so idk)

@ankitamandal18 5 жыл бұрын

synthetic division

@GGJeff 3 жыл бұрын

I was so confused on what to do if the equation did not factory thank you so much

@brianmclogan 3 жыл бұрын

You are very welcome

@krspypatriot3545 3 жыл бұрын

cheddar bob really out here teaching us what our teachers dont

@jjsloan1035 4 жыл бұрын

Thank you so much

@Youreclecticoldersister Жыл бұрын

How do you figure out how many positive and negative real numbers there are?

@purnasherpa7386 6 жыл бұрын

we can use remainder theorem to check whether it a factor or not?

@brianmclogan 6 жыл бұрын

of course

@zplusacademy5718 2 жыл бұрын

Extremely beautiful effort and execution dear sir....I enjoyed your way of solving ❤️🙏❤️❤️🙏🙏❤️❤️❤️❤️❤️❤️❤️❤️❤️🙏🙏🏡🙏❤️

@brianmclogan 2 жыл бұрын

So happy to help!!

@CJ-ph7rn 3 жыл бұрын

Thank you very much 😍 This helped me so much thankyou

@trkingdavid4943 4 жыл бұрын

well explained

@sarahzakaria685 4 жыл бұрын

This helped sm ty

@Sam_lifts504 3 жыл бұрын

what if there is no alternating signs in the equation ?

@eteafn 4 жыл бұрын

thanks man i have a hw quiz tmrw

@cynthiacastaneda7481 5 жыл бұрын

I'm not sure if you're responding to comments anymore but what if the polynomial isn't factorable and isn't a quadratic?

@aera151 5 жыл бұрын

I know this is an old comment but in general, you solve for the p's and q's. You can also use your calculator to input the equation for y= (equation here) to see where the x-intercepts are.

@yamyam8717 7 жыл бұрын

thank you

@brianmclogan 7 жыл бұрын

you are very welcome!

@icee562 5 жыл бұрын

you guys have no idea how useful this is until you take ODEs

@caamster23 2 ай бұрын

king is saving me for finals love u bro 💯💯

@highteirgod 8 ай бұрын

everyone in my classroom is watching this rn, right before a quiz

@alhamdulilah4950 4 жыл бұрын

what a smart teacher

@williamtoothpick6033 5 жыл бұрын

7:08 F

@blck_gann 2 жыл бұрын

But how will you graph it?

@gabbydoodle1 4 жыл бұрын

3:36 Wouldn't the -6(-x)^2 become +6x^2, not -6x^2 ??

@tlee-gc6ym 4 жыл бұрын

No, it’s -6x^2, P.E.M.D.A.S., you do the exponents first

@MathLab4u 3 жыл бұрын

math teachers cubics as well You might look at some examples kzfaq.info/get/bejne/n9iTjcJ-ltOXeWw.html

@johnnymcgillen8295 6 жыл бұрын

could someone please explain to me why you get 3 or 1 positive zeros?

@brianmclogan 6 жыл бұрын

descartes rule of signs, again above most freshman classes, taught this for my pre-calc class

@sawyerchiles91 6 жыл бұрын

for every imaginary zero, there is another imaginary one which is it's conjugate. Because of this, there must be an even number of imaginary zeros and if you reduce the number of positive or negative zeros by an odd number, there would be an odd number of imaginary zeros, which doesnt work.

@mac9733 6 жыл бұрын

Say you have ++++ -, you'd have 4 positive and 1 negative. Would I still have to subtract an even number from the four zeros and include it?

@aishwary2047 6 жыл бұрын

hi sir, i have an doubt why you take +-10 but not taken other values, please comment

@brianmclogan 6 жыл бұрын

it is plus or minus all the possible rational zeros, I usually write parenthesis, looks like I got lazy

@dawgtora.sushii 4 жыл бұрын

frickin bless his soul

@TheSuperJLA 3 жыл бұрын

better than my college professor

@habtiegetnet3281 3 жыл бұрын

thanks

@fatwebb8008 5 жыл бұрын

Bro we’re learning this in Math 3 And it’s such a hard process

@keaedo394 5 жыл бұрын

You'll get the hang of it mate... higher math classes like calculus will will have more complex processes

@MathLab4u 3 жыл бұрын

math teachers cubics as well You might look at some examples kzfaq.info/get/bejne/n9iTjcJ-ltOXeWw.html

@lucky-mud 4 жыл бұрын

holy shit people in the US actually learn a lot. I'm in Argentina (senior year) and we're just now starting with derivatives. And... with that shitty math, I'm trying to take the SAT (you can imagine my results).

@Fightclub1995 6 жыл бұрын

Why not plug in the numbers to check if its zero instead of division?

@brianmclogan 6 жыл бұрын

nothing wrong with that way as well

@Fightclub1995 6 жыл бұрын

Elizabeth McGurty Im talking about plugging in the found possible rational roots; 10, 5, 2, 1.

@Fightclub1995 6 жыл бұрын

Im talking about the long division part in the video. Brian finds some possible roots 10,5,2,1 and he proceeds by checking if 1 is a root by using long division, which can be allot of work (and you might make some errors). I suggest to just check if f(1)=0, which is just some basic arithmetic.

@Fightclub1995 6 жыл бұрын

Elizabeth McGurty Remember you can use: if f(a)=0 then f(x)=(x-a)g(x) , where g is polynomial of 1 degree less than f.

@hinalbalia6629 5 жыл бұрын

usually using synthetic division is quite easier than substitution. Because the x cubed terms can start to make big numbers and a higher chance you make a mistake. Honestly, both ways work, and it can be based on preference, but most, as well as I, would recommend synthetic division to check.

@haydenmaeg.mortel1309 4 жыл бұрын

Salamat sa tulong mo🤣

@ragyebeid9786 4 жыл бұрын

6:22 you did 1•1=1 then added that to -5 but kept it as negative 5

@sledge2742 3 жыл бұрын

his hair left him because nothing can survive being near his brain for too long

@samtorres515 3 жыл бұрын

i love u for this

@andrejohndechoso8445 3 жыл бұрын

I don't get it :

@ghader2375 5 жыл бұрын

can I ask how the real zeros 3 and 1 came from?

@fatmaelzahraaelsheimy8759 4 жыл бұрын

You always have the possibility of having imaginary roots, however, you can't really detect them from descarte's rule of signs. And since the imaginary roots come in pairs( imaginary and its conjugate), you will either have 3 positive real roots or 1 positive and 2 imaginary. Hope this helps

@keneagu916 4 жыл бұрын

@@fatmaelzahraaelsheimy8759 in laymans terms please

@gustavoignacioduarte2362 4 жыл бұрын

3 or 1 aren't roots but the quantities of roots: this polynomial might have 3 or 1 real rootS.

@klarawelson2358 6 жыл бұрын

CAN YOU PLEASE SEND ME YOUR WORKSHEETS FOR GRAPHING POLYNOMIALS

@brianmclogan 6 жыл бұрын

not sure what copies I was using

@Fightclub1995 6 жыл бұрын

Eisenstein theorem is also usefull

@brianmclogan 6 жыл бұрын

👍

@myra9130 3 жыл бұрын

8:51 how did you get 4 as your B here?

@HeloisaChalom 3 жыл бұрын

i think he messed up the 4^2 on the b inside the square rt

@HeloisaChalom 3 жыл бұрын

but it didnt matter bc it would be squared anyways

@navinkumarshah2289 4 жыл бұрын

96x^3-380x^2-(149-292√2)x+(29+146√2=0. sir i need zeros of this cubic equation. thank you sir for above amazing video.

@aishwary2047 6 жыл бұрын

i dont think so that it is right or valid for all equations

@brianmclogan 6 жыл бұрын

nope works for all polynomials, but is not the most efficient method, should look to factor first or use a graphing calculator

@aishwary2047 6 жыл бұрын

if i give you a equation in which square term is missing or x term is missing then how can you solve it

@aishwary2047 6 жыл бұрын

there is one method which is given in quora but i cant understand and i think it is more correct for all cubic equations

@aishwary2047 6 жыл бұрын

in quora , like we solve quardatic which you have in ending to solve quardatic in the same way there is a formula for solving cubic and many things is given there, i think you should see that

@reyazulwarsi4466 6 жыл бұрын

I am trying to solve 4x^3 + 2x +1 =0 . But I am not able to solve it can you help me

@brianmclogan 6 жыл бұрын

How are you trying to solve it, did you try the quadratic formula, it is not factorable across real numbers. mathway.com will give you the answer

@reyazulwarsi4466 6 жыл бұрын

Brian McLogan, sir I am trying to solve it with rational zeros test method learnt from your video . And I don't have answer. Actually I have to find the local minimum for f(x) = x^4 + x^2 + x -1 . On differenting it gives 4x^3 + 2x + 1.

@kenanwood6916 6 жыл бұрын

reyazul warsi let x=-1/2.

@KumaMech 6 жыл бұрын

the roots for that equation are not rational. it only has one real root and that is approximately x = -0.38546

@mr.punkie5872 5 жыл бұрын

Help my homework says “Identify the number of solutions or zeroes”

@brianmclogan 5 жыл бұрын

same as the degree via the Fundamental theorem of Algebra

@mr.punkie5872 5 жыл бұрын

Brian McLogan but when I do the synthetic division, no numbers gives me 0, maybe I’m doing something wrong but I don’t get it, do you have a video about that?

@Tech_Gamers 4 жыл бұрын

This is calculus? We are supposed to learn this at grade 8 in india😭

@urbicide_if 3 жыл бұрын

THANK YOU 🙏🏼

@bufflarrythegreat1145 3 жыл бұрын

Why is zero always hiding???

@wiliwiliful 4 жыл бұрын

Thanks so much my teacher wasn't so professional than you

@ROBOOTDANCING 4 жыл бұрын

Or -1 5 2 is the answer

@Clouded_Days 4 жыл бұрын

I'm just not understanding this...

@aryamazandarani6373 5 жыл бұрын

why am i learning this algebra 2 shit in precalc

@sarahzakaria685 4 жыл бұрын

My daddy my superiro u helped I’m abt to ace this test!!😘

@rameshjaykar902 3 жыл бұрын

i know dont know when u guys are being learned but India we will be taught in 7th class i.e.15years old

@johnnymcgillen8295 6 жыл бұрын

I am a mere freshman in high school so I don’t really get this at all

@brianmclogan 6 жыл бұрын

yes this is an advanced problem for my pre-calculus class

@rajeshrajak8258 6 жыл бұрын

Johnny mcgillen u r really foolish

@rajeshrajak8258 6 жыл бұрын

I have truely understood the problem

@mr.zombified3378 6 жыл бұрын

I’m a freshman in highschool and I’m doing this stuff

@johnnymcgillen8295 6 жыл бұрын

nobody asked you

@nonehandle688 4 жыл бұрын

This guy demonstrates all that's wrong with math classes around the world. There's NO CONNECTION between this and anything before this. The only people who "get" this are those who already get it. I feel sorry for anyone who has to take this class.

@brianmclogan 4 жыл бұрын

Kai this is a snippet of instruction from my class. Not intended to show the full connection or even understanding. I understand if that is what you were looking for, this video falls short. Sorry about thst

@calebwright1052 5 жыл бұрын

This video was helpful sure, but also he looks a lot like cheddar bob from 8 mile

@nextgenfootball69420 4 жыл бұрын

Lol he also looks like food ranger

@aishwary2047 6 жыл бұрын

i will change if i give you cubic equation you can never solve it by this methods

@brianmclogan 6 жыл бұрын

this is a cubic equation, this works for all polynomials, again most problems use a calculator or graphing calculator

@thealmightyoppai1670 Жыл бұрын

The thumbnail is wrong . I thought it was perfect square trinomial

@jerushatallapally3940 3 жыл бұрын

who watching this in 2020 bc they have pre calc

@jacksongatens2419 3 жыл бұрын

Anyone else watching this during their test?

@eelisattibabu7078 4 жыл бұрын

I don't understand anything 😔

@carealoo744 4 жыл бұрын

I have no idea what the heck is going on.

@belleliu7921 4 жыл бұрын

7:18 listen closely haha

@localbiggin1645 4 жыл бұрын

i played that bit so many times and dont hear a thing. What did the students say?

@zabrim8046 2 жыл бұрын

کوی برام

@jessicaquintona371 3 жыл бұрын

Have you paid your daily respects to our savoir?

@bhardwajhouse5692 3 жыл бұрын

Of which standrd is he teaching?😂

@etowngftddummy 2 жыл бұрын

I know it's not English class, but don't use apostrophes to make things plural. Zero's would be zeroes (without the e it's zeros). It bothers me more than I wish it did.

@imightfixit 3 жыл бұрын

too fast

@melight123 4 жыл бұрын

Show me a ZERO a real reason ZERO is ZERO number all I see 👀 is ocular O00000 please do white board with scribed real ZERO s ..O for past they couldn't tell the difference between 0ocular from alphabet 0 and a number form ...

@dynxmit3official920 4 жыл бұрын

He would look very handsome with hair.

@eelisattibabu7078 4 жыл бұрын

Stupid

@douglasservesjesus 3 жыл бұрын

Jesus Christ is coming soon, God is telling y'all to repent from your sins and live a life for him so you wont get left behind when he comes back and take his people.

@happysunshine5069 3 жыл бұрын

WHY are you commenting this on calculus videos??????

@douglasservesjesus 3 жыл бұрын

@@happysunshine5069 because people are heading to hell and people need to accept Jesus Christ into their life because he is good, his grace is sufficient and his love is unconditional

@happysunshine5069 3 жыл бұрын

@@douglasservesjesus Yeah but why

@tommykelly6833 3 жыл бұрын

Why do you make things so complicated for your students? Why do you have to shout at them?I'll tell you why it's because you are not comfortable in your surroundings!!! Glad my kids are not in your class!!!

@Kevinwelch2001 3 жыл бұрын

He’s probably the best example for an enthusiastic and helpful teacher.