Introduction to Polynomials

We have seen a nice variety of algebraic equations by now, so let's hone in on a specific kind that we will be working with a lot. These are called polynomials. Let's quickly define what they are and some of their properties, so that we can learn all about how to solve them in the next few clips!
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[@amchedli]

Hey Prof. Dave just a suggestion: what if every 5-10 clips you had a small review quiz of 10-15 questions. It would help with further comprehension as well as retention of material for your students.

[@numbobot531]

Great Idea!

[@RajanLakhara]

Right

[@boopteehee6663]

I just got an advert saying "still searching KZbin for maths help? Are the videos from 2006 really helping?". If only they knew...

[@ChainsawChristmas]

are they?

[@calebobaseki]

​@@ChainsawChristmasyes they are

[@Dracarys895]

😁

[@lizabarabanova8345]

Read the definition in Wikipedia and compared it with yours. Yours is way much clearer. I just admire the quality of your explanations and videos in general. Super professional!

[@arkan7rb]

i really dont know how to thank you Pro Dave, i wish i could support you but i live in Yemen so the least is to sub share and like god bless you greetings from Yemen

[@melodyjackson6617]

thanks, professor Dave

[@yuugi5185]

I feel like.... im straying further away from reality

[@ian.ambrose]

No please come back, math will only get more fun as you go further into it.

[@jayw8726]

"Lets put that reverence in to our pockets!".... yes sir!!

[@dontstealmydiamondsv3156]

Thanks once again!

[@science-y9209]

Woah.. my mind is blown.. I mean..how you literally covered these important things in just 5 minutes

[@thegoodlydragon7452]

What does the sub N part mean?

[@thegoodlydragon7452]

A little explanation of the beginning part with the subscripts would help clarify the rest of the video.

[@hashmarker4994]

Those are subscripts. They are there to show a possible template of the polynomial. n can be any number here example in the quadratic polynomial 2x^2 + 3x +7 , n is 2 .consider it like this x^0 then n= 0 , x^1 then n= 1, when x^n then n= n, n is just a figure to represent any number which is the highest power of the variable in that equation. the subscript just denotes the count of expressions ex: 2x + b has 2 expression surrounding the +, the 2x and the b , so b is the 0th element and 2 the 1st element. Which conveniently also happens to be the power of the variable of the respective coefficients.

[@NickHope]

I guess those subscripts are just like labels attached to the preceding character, and we don't do any mathematical operation with them. 'a' is not the same in each part of the polynomial, but instead of writing 'a', 'b', 'c' etc., he writes, for example, 'a sub (n-1)', meaning "the factor 'a' that belongs in the part of the polynomial where x is raised to the power (n-1)." Likewise, 'a sub (n-3)' means "the factor 'a' that belongs in the part of the polynomial where x is raised to the power (n-3)." I might be wrong. I wish Dave had explained what they are rather than just throw them in there. It's the first time this brilliant course has me lost.

[@MCGR]

trying to save myself rn, thanks for the playlist

[@j.clowers7223]

Will there be a part two?

[@ProfessorDaveExplains]

the next 6 clips are about polynomials!

[@princesselyzajeanetamayao7489]

2x^2+4x+10 2(-1)^2+4(-1)+10 2-4+10-----USE PEMDAS =12 is the correct answer

[@necrom6858]

In PEMDAS, addition and subtraction and multiplication and division are both done left to right. Even if we used your logic it would still be 2 - 14 which is -12 not 12.

[@melodyjackson6617]

totally laughed at the intro

[@phurpatshering9342]

No need to laugh coz u can't even make it

[@DanielleDagg]

There may or may not be a part 2 of this video

[@syedaqibfida]

Hi Prof Dave! I am confused regarding the real life application of the polynomials. What kind of real life problem involves modelling by using higher exponents of the same variable, x and then slowly decreasing them forming a polynomial?

[@an-ny-ous6-87-5t6--..._....]

Hey there, Real-life applications of polynomials are more common than you might think. Let's break it down: **1. Physics:** When you throw a ball into the air, its height can be modeled by a polynomial function. The equation includes terms for gravity (a constant) and the initial velocity of the ball. **2. Engineering:** Structural engineers use polynomial equations to design bridges, buildings, and other structures. These equations help predict factors like stress, strain, and load distribution. **3. Economics:** In finance, polynomial functions are used to model things like supply and demand curves, cost functions, and revenue functions. This helps businesses optimize their operations and maximize profits. **4. Medicine:** Polynomial equations are used in medical research to model things like growth rates of tumors, drug absorption rates, and population growth of diseases. **5. Computer Graphics:** Graphics software uses polynomial equations to render 3D objects and animations. These equations help determine the shape, position, and movement of objects on the screen. So, whether you're calculating the trajectory of a rocket, designing a skyscraper, or analyzing market trends, polynomials are there, quietly doing the heavy lifting behind the scenes. Hope that clears things up for you!

[@yamatanoorochi3149]

4:33 I shall sacrifice my calculator to my lord and savior dr dave

[@Gd_Monsterforce]

To simplify it or make things easier, (2x^2 + 4x) must be -10 because 2x^2 + 4x + 10 = 0 so, try and make 2x^2 + 4x = -10

[@chourouk-gr9qg]

thank u

[@OkSid300]

Why am I feeling like I am going to get rekt in a next part?

[@pradeepsharma8048]

WHAT ???? ALL WHOLE NUMBERS ARE POSITIVE .. ISN'T IT ME DAVE ...

[@geohayek9943]

i wish you're my teacher

[@tGoldenPhoenix]

Thank you

[@tGoldenPhoenix]

Done this lesson.

[@vedhamara6748]

are you penguinz 0's brother

[@timsn274]

Sixth degree is sextic, seventh is heptic, eighth is octic.

[@darwinvironomy3538]

Nineth is nonic Tenth is decic

[@savant6842]

🤫

[@RodMigz08]

Aint this a aphex twin song

[@mamadwali4278]

❤❤❤

[@siddhantpalyekar6248]

I'm still confused with the order of operation rules

[@gayathribhargavibandi3459]

The answer is -1+2i and -1-2i

[@petricor1420]

4:10 Wrong word bozo, it’s GENIUS, 🙄

[@amirmagonid3386]

Reverence and worship the Lord my God and Him alone do I serve. You may mock Him now, but you will stand before Him as you are judged by Him eventually.

[@ProfessorDaveExplains]

This is a math tutorial, chief.