Master - How to find the zeros of a polynomial function by factoring and determine multiplicity

Рет қаралды 133,135

Күн бұрын

👉 Learn how to find all the zeros of a polynomial. 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, we first equate the polynomial to 0 and then use our knowledge of techniques of factoring polynomials to factor the polynomial. After we have factored the polynomial, we can then use the zero-product property to evaluate the factored polynomial and hence obtain the zeros of the polynomial.
Recall that the zero-product property states that when the product of two or more terms is zero, then either of the term is equal to 0.
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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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👨‍👩‍👧‍👧 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: 98

@audreyalvarez8576 4 жыл бұрын

watching your channel has taught me more than my actual teacher. Thank you

@cbuckets3024 3 жыл бұрын

Right school is so pointless

@ubeking101 Жыл бұрын

The honest truth....

@amberlouize127 8 жыл бұрын

Clear instructions without shortcuts, finally! Thank you!! Now I just need to practice these and see if I get the same answers...

@brianmclogan 8 жыл бұрын

keep working hard, happy to be able to help you out!

@tinazeimaran3863 6 жыл бұрын

Your videos are the biggest help to understand math problems. Thanks Mr McLogan.

@brianmclogan 6 жыл бұрын

you are very welcome Tina!!

@MATHZZZZZZZZZZ 3 жыл бұрын

number one Brian best teacher

@noelinatombora7114 5 жыл бұрын

You're the best in math!😊thank so much! I I was confused but now I understand😍

@norve3306 3 жыл бұрын

Thank you for this educational content 🤎 From Egypt 🦅🖤

@ghosty4215 5 жыл бұрын

YES! Thank you so much! I learned so much after watching this video! Now I can answer my dads math questions!!!

@courtneysoliz7747 5 жыл бұрын

thank you SO much for covering practice problems!

@WhiteChocolate444 2 жыл бұрын

Your videos are great, it's the enthusiasm!!! Thank you!

@tjmaster7779 4 жыл бұрын

Thanks soooo much Ive been so frustrated because I couldnt find any videos explaining what I needed help with. Now I think i understand. Thanks again!

@micahsigrest689 3 жыл бұрын

So helpful. Your great, thanks!

@SairagMaram 3 жыл бұрын

This was super helpful! thank you.

@DenisPinsonnault 2 жыл бұрын

Thanks for your work. I didn't get the same answer solving the following example: f(x)=-2x^4 - 2x^3 -2x^3 (x + 1) = 0 x_{1, 2, 3} = 0, x_4 = -1

@ramjiswaminathan6566 3 жыл бұрын

Tq so much !! Was very easy to learn it quickly n helped me a lot in Math..tq once again👍👊

@tigistworku2494 4 жыл бұрын

Thank you very much. You are so fantastic

@user-fv7om7qf4o 2 жыл бұрын

Thank you!

@annarasumanara2004 3 жыл бұрын

Thank you so muuuuuuuch❤️

@sierascorner27 6 жыл бұрын

i love your videos! they save me in math!!

@brianmclogan 6 жыл бұрын

so happy to be able to help you out! keep up the hard work

@deathstramy7272 Жыл бұрын

Really good format wasnt finding what i needed until this video

@brianmclogan Жыл бұрын

So happy to help!!

@creep4989 8 жыл бұрын

thank you! im going to download this video. Helped me a lot

@brianmclogan 8 жыл бұрын

awesome, happy to be able to help you out!

@claireyewy 2 жыл бұрын

a concern with example 7, if you factored out -2x^3 then shouldn't 1 be positive? -2x^3(x + 1), you will still distribute it inside so if the sign of '1' is wrong, then the whole eqaution would be kinda off. just my opinion. please do explain, if anyone would care to :))

@buffbeanburrito 6 жыл бұрын

Very helpful, thank you👍

@brianmclogan 6 жыл бұрын

you are most welcome!

@rain_reverb Жыл бұрын

I don't know why I find all so hard to solve but I was here for the quadratic and cubic one ur way to solve is easy all I'm gonna do is more practice then I will be easily able to verify the zeroes and finish my ch 😮‍💨❤️❤️ anyways lots of love sir 🤗

@typicaljed4513 4 жыл бұрын

Help a lot👍

@vanshuvibes8095 7 жыл бұрын

helped me a lot to understand ...

@brianmclogan 7 жыл бұрын

great! happy to be able to help

@stellaflair5011 4 жыл бұрын

Thank u, be our math teacher

@thomasa2041 5 жыл бұрын

How would I find the zeroes of a polynomial that can't be grouped like the ones in this video?

@juliencloud23 3 жыл бұрын

Yeah, I wish he had picked some out that were more complex. A lot of these seemed more straightforward than the ones I'm actually having to learn to do.

@f0x106 5 жыл бұрын

My teachers for 2 years teached me to make those equations on calculator modes

@yulxisy 4 жыл бұрын

what about the ones that dont start with f(x)?

@sydneyisabel8046 6 жыл бұрын

THANK YOU SO MUCH!

@brianmclogan 6 жыл бұрын

you are very welcome!

@leslyannboco1883 4 жыл бұрын

thank yoooou！

@kniferock649 7 жыл бұрын

Thx got it in the first 3 min very helpfull

@brianmclogan 7 жыл бұрын

perfect! happy to help

@greatEras Жыл бұрын

OOOOOh thank uuuuuuuu!

@kiki1x7 6 жыл бұрын

math god! love your videos

@brianmclogan 6 жыл бұрын

thanks!

@rBJ817 6 жыл бұрын

You're awesome man

@brianmclogan 6 жыл бұрын

haha probably

@sevzn 3 жыл бұрын

you are the reason i can pass trig

@miguelangelhernandez6745 5 жыл бұрын

For the firs and second questions, since each one is odd, does that mean it crosses the x-axis once?

@brianmclogan 5 жыл бұрын

yes if the function has an odd degree it must cross the x-axis at least once

@alexandritta23 8 жыл бұрын

Awesome video! Thank you for taking the time :)

@brianmclogan 8 жыл бұрын

you are very welcome! happy to help

@whatsupwithtorii 7 жыл бұрын

omg thank you sooooooooooo much!!!!!!

@brianmclogan 7 жыл бұрын

you are very welcome!

@christietoole4279 5 жыл бұрын

In the 5th problem, is x= squ rt -3 and x= squ rt 2 real zeros or no? Why are some rt answers real zeros and some are not? Like x= cubed rt -5?

@danaschannel4593 5 жыл бұрын

I do have a question sir?!...what is the important of knowing that if the numbers are even or odd ? Is is because it tell us the way that it is going to across the x-axis ? If it was curved or straight....thanks

@brianmclogan 5 жыл бұрын

do you mean the multiplicity? then yes even or odd tells the behavior

@isabellaa.2184 7 жыл бұрын

I appreciate the help! But sir, you seem out of breath! Don't be in a rush or nervous. Thanks!

@brianmclogan 7 жыл бұрын

haha thank you, not sure why I am like that for this video, glad it helped though

@gunny-ex7vs 2 жыл бұрын

W video.

@kimkatbar 6 жыл бұрын

You saved me omg

@brianmclogan 6 жыл бұрын

happy to help

@ezra2370 4 жыл бұрын

can u do it with more space plssssssssss

@sujathabanoth4129 7 жыл бұрын

it so nice to help us but you can you say polynomial of long division

@brianmclogan 7 жыл бұрын

You want a video showing how to find the zeros using long division?

@aarajput5721 6 жыл бұрын

x^3-2x^2+4x-3

@brianmclogan 6 жыл бұрын

not factorable across real rational numbers, look to graph it

@angelina-cp6jn 2 жыл бұрын

couldnt you have gotten i sqrt2 for the square root of -2

@qureshiowais6951 5 жыл бұрын

wait how x =x^2 how how ??????? if x is 2 means 2 =2^2 so but 2 != 4 ?

@alexleon3934 3 жыл бұрын

Everyone praises Sal Khan for his smarts, but I understood this concept better on here than on Khan Academy. Thanks!

@aashsyed1277 3 жыл бұрын

NO BRIAN IS BETTER

@sandeshkumari4807 6 жыл бұрын

Can you please tell us slow

@brianmclogan 6 жыл бұрын

Sorry, sometimes I get excited and talk really fast

@lazeonhd2616 4 жыл бұрын

Its kinda difficult to understand, due to teachers having they’re own method of teaching, i cant catch up to this guy.

@xxTAARGUS 4 жыл бұрын

I would say the more teachers you can watch explaining the same thing then the better.

@isabelcustodio3210 4 жыл бұрын

True! I would say avoid watching so many to prevent confusion. I hope you managed to pass

@juliencloud23 3 жыл бұрын

That third one made no sense when you changed that x^4 to x^2. Wish you'd been a bit more thorough on that. I understood the rest.

@claireyewy 2 жыл бұрын

a tip, what i would do is completely substitute a single variable. since there are both x^4 and x^2 in the eq, i could take the x^2 (since it is the somehow common factor) and substitute it into a different letter. like this: x^4 + 4x^2 + 4 = 0 Legend: x^2 = a (x^2)^2 + 4(x^2) + 4 = 0 then substitute, a^2 + 4a + 4 = 0 and continue on with what he does, i don't know if this is more confusing but it's just what i do. have a nice day :))

@prinreborn 6 жыл бұрын

zero is an even number

@brianmclogan 6 жыл бұрын

correct

@aphrodeity5992 3 жыл бұрын

you look healthier here

@gypsy_angela 3 жыл бұрын

2020?

@jeffreybals4430 2 жыл бұрын

I think I'll try brain surgery instead... 🙃

@brianmclogan 2 жыл бұрын

👀👀👀

@vishakhabauddha1837 3 жыл бұрын

Hallo I am Indian... And you???

@joeyb649 6 жыл бұрын

Top right one is wrong, the square root of 2, and the negative square root 2, with a multiplicity of 2 is the answer.

@brianmclogan 6 жыл бұрын

it is the square root of -2 so not real root

@bhogsinghnayak8662 5 жыл бұрын

Pliz teach slowly

@kamiiu 5 жыл бұрын

Why does the school system even teach us this? Most of us will never use factoring in our entire life. This is a waste of precious time.

@neji434 5 жыл бұрын

I guess to test your ability to understand and maybe solve irl problems in the future idk I’m getting bored

@naveensharma5093 5 жыл бұрын

Sir can u speak hindi

@prembirsingh3070 6 жыл бұрын

u laugh so much rather than solve the doubts

@brianmclogan 6 жыл бұрын

hmmmm interesting

@jeffreybals4430 2 жыл бұрын

Omg. 🤢

@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.

@kimwiha4400 3 жыл бұрын

We are here for maths man😂😂 Out of lesson