How to Determine All of the Zeros of a Polynomial
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- čas přidán 9. 09. 2013
- 👉 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.
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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...
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#polynomials #brianmclogan
imagine taking his math classes in high school, you'll be set for life
dude you have no idea. Im in college and I still watch his vids
@@aebious8886 😂
Cupcake
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.
math teachers cubics as well
You might look at some examples
czcams.com/video/ircZ_M1m3I8/video.html
Was about to jump out a window and then I found this. This man makes me pass algebra 2.
learned more in three hours from him than in three months of my 110 class
math teachers cubics as well
You might look at some examples
czcams.com/video/ircZ_M1m3I8/video.html
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
Calculus is better than this.
There is still review in Precalculus.
I’m doing this in college Algebra 😂😂
I did this in advanced stats
Precalculus is algebra 2 lol
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!
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
@@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!
@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!
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
My teacher is absolutely awful, and I am so glad these videos exist. I would not be passing Pre Calc. without them.
DUDE THANK U. i wouldn’t be passing online precalc without this man
i'm developing such a crush on this man.
i feel u
@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:
czcams.com/video/2w1lXuM6pbA/video.html
thx i had the same question epic
Wonderful, thank you so much
a life saver! thank you!
I had the exact same question as well. my thanks and appreciation.
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
this video clarifies my understanding at a conceptual level. Thank you Mr. McLogan !
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
Very Good, Brian McLogan
Like legit .. thank you soooo much.. i was struggling in that the whole term 😭😭😭
you are very welcome! happy to help
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)
How's Becky doing?
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...
appreciate it. I 100% agree
6:55 what is this method you used ? and what for ?(from UK we might use different methods so idk)
synthetic division
thank you!
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?
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!
Thank you! I'm at home for school for math right now your videos have helped a lot
Just what I needed.
This is very helpful, i had problems with finding eigen-values of an system and simply was not good enough to find them zeros...
king is saving me for finals love u bro 💯💯
Thank you for this beautiful mathematical video.
I was so confused on what to do if the equation did not factory thank you so much
You are very welcome
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.
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🤔🤔🤔
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
simple and genial thanks.
we can use remainder theorem to check whether it a factor or not?
of course
everyone in my classroom is watching this rn, right before a quiz
cheddar bob really out here teaching us what our teachers dont
Thank you so much
I'm not sure if you're responding to comments anymore but what if the polynomial isn't factorable and isn't a quadratic?
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.
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.....
Thank you very much 😍
This helped me so much thankyou
How do you figure out how many positive and negative real numbers there are?
3:36
Wouldn't the -6(-x)^2 become +6x^2, not -6x^2 ??
No, it’s -6x^2, P.E.M.D.A.S., you do the exponents first
math teachers cubics as well
You might look at some examples
czcams.com/video/ircZ_M1m3I8/video.html
Extremely beautiful effort and execution dear sir....I enjoyed your way of solving ❤️🙏❤️❤️🙏🙏❤️❤️❤️❤️❤️❤️❤️❤️❤️🙏🙏🏡🙏❤️
So happy to help!!
could someone please explain to me why you get 3 or 1 positive zeros?
descartes rule of signs, again above most freshman classes, taught this for my pre-calc class
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.
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?
thank you
you are very welcome!
7:08 F
you guys have no idea how useful this is until you take ODEs
hi sir, i have an doubt why you take +-10 but not taken other values, please comment
it is plus or minus all the possible rational zeros, I usually write parenthesis, looks like I got lazy
This helped sm ty
Why not plug in the numbers to check if its zero instead of division?
nothing wrong with that way as well
Elizabeth McGurty Im talking about plugging in the found possible rational roots; 10, 5, 2, 1.
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.
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.
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.
thanks man i have a hw quiz tmrw
what if there is no alternating signs in the equation ?
what a smart teacher
Bro we’re learning this in Math 3
And it’s such a hard process
You'll get the hang of it mate... higher math classes like calculus will will have more complex processes
math teachers cubics as well
You might look at some examples
czcams.com/video/ircZ_M1m3I8/video.html
But how will you graph it?
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).
frickin bless his soul
I don't get it :
well explained
thanks
better than my college professor
his hair left him because nothing can survive being near his brain for too long
can I ask how the real zeros 3 and 1 came from?
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
@@fatmaelzahraaelsheimy8759 in laymans terms please
3 or 1 aren't roots but the quantities of roots: this polynomial might have 3 or 1 real rootS.
Salamat sa tulong mo🤣
CAN YOU PLEASE SEND ME YOUR WORKSHEETS FOR GRAPHING POLYNOMIALS
not sure what copies I was using
i love u for this
Eisenstein theorem is also usefull
👍
8:51 how did you get 4 as your B here?
i think he messed up the 4^2 on the b inside the square rt
but it didnt matter bc it would be squared anyways
6:22 you did 1•1=1 then added that to -5 but kept it as negative 5
i dont think so that it is right or valid for all equations
nope works for all polynomials, but is not the most efficient method, should look to factor first or use a graphing calculator
if i give you a equation in which square term is missing or x term is missing then how can you solve it
there is one method which is given in quora but i cant understand and i think it is more correct for all cubic equations
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
I am trying to solve 4x^3 + 2x +1 =0 . But I am not able to solve it can you help me
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
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.
reyazul warsi let x=-1/2.
the roots for that equation are not rational. it only has one real root and that is approximately x = -0.38546
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.
i know dont know when u guys are being learned but India we will be taught in 7th class i.e.15years old
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.
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
Thanks so much my teacher wasn't so professional than you
My daddy my superiro u helped I’m abt to ace this test!!😘
Help my homework says “Identify the number of solutions or zeroes”
same as the degree via the Fundamental theorem of Algebra
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?
This is calculus? We are supposed to learn this at grade 8 in india😭
Or -1 5 2 is the answer
THANK YOU 🙏🏼
Why is zero always hiding???
This video was helpful sure, but also he looks a lot like cheddar bob from 8 mile
Lol he also looks like food ranger
I'm just not understanding this...
Anyone else watching this during their test?
The thumbnail is wrong . I thought it was perfect square trinomial
why am i learning this algebra 2 shit in precalc
I am a mere freshman in high school so I don’t really get this at all
yes this is an advanced problem for my pre-calculus class
Johnny mcgillen u r really foolish
I have truely understood the problem
I’m a freshman in highschool and I’m doing this stuff
nobody asked you
who watching this in 2020 bc they have pre calc
i will change if i give you cubic equation you can never solve it by this methods
this is a cubic equation, this works for all polynomials, again most problems use a calculator or graphing calculator
کوی برام
7:18 listen closely haha
i played that bit so many times and dont hear a thing. What did the students say?
Have you paid your daily respects to our savoir?
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.
I have no idea what the heck is going on.
I don't understand anything 😔
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 ...
Of which standrd is he teaching?😂
too fast
He would look very handsome with hair.
Stupid
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.
WHY are you commenting this on calculus videos??????
@@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
@@douglasservesjesus Yeah but why
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!!!
He’s probably the best example for an enthusiastic and helpful teacher.