Introduction to Polynomial Functions (Precalculus - College Algebra 27)

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What polynomial functions are, how they are organized, and their important features.

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One of the best professors here on KZbin, besides one of the best playlists ever

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Professor Leonard, please do Trigonometry playlist. 🥺 Your channel is awesome! You helped me so much!!!

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I'm so happy for you, mr. Leonard. Everyone's just praising you, you're doing such an amazing job. You must feel very accomplished as a teacher. Truly a Godsent to me. I learned all from pre-alg to here from you. I'm so blessed to be able to study with you. I'M SO EXCITED for calculus, you don't even know!!

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Professor Leonard, thank you for a mammoth introduction to Polynomials and Non -Polynomials, leading terms, coefficients and constants in Precalculus/College Algebra.

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I passed (and actually understood) calc 2 this summer thanks to your videos my man.

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You're such an inspiration to me professor! I am a teacher in the making and I sometimes find myself struggling to explain some of these concepts to my students in a "simple" way (I guess that's what happens when you study math at UNI for too long...) . Your explanations have been really helpful to me in finding my own way to teach math - I cannot thank you enough for that. All the love.

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I don't know I think it's more about the teacher. As Albert Einstein said: "If you can't explain it simply, you don't understand it well enough."

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@@petrmasek4506 I don't agree with that quote at all, even if Einstein said it (it is a logical fallacy called appeal to authority). There's so many influential philosophers who contributed greatly in their fields but were awful writers, meaning that they could not explain their ideas in layman's terms even if they understood it very well. Examples are Kant, Kierkegaard, and several continental philosophers.

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Thank you Leonard. I know you have to finish pre-cal, statistics, and then lin alg. I’m rooting for you and I’m excited for the lin alg that will eventually come.

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I have taken precalculus and failed it 2 times. You're videos have helped me so much! Please continue uploading, I hope you can also cover matrices as that is what I struggled the most in precalc. Thank you so much

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I was wondering how many videos would be there in total? I assume you'll be covering Trigonometry and Logarithms too? Anyways a BIG THANK YOU for everything you've done till now

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Prof Leonard, can you please do videos on Linear Algebra? Your the absolute best at teaching, I need you for it!!

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One of the best maths teachers, god of maths....🤩

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Great timing.. I'm almost done with the Intermediate Algebra series, and was hoping you would be able to get back to adding more to this Precalc series soon. Any chance you could tell us how many videos you expect to be in this series, all total?

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We want complete discussion on how to find domain and range of various functions and functions of function

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I may support you for calculus 1, 2, and 3.

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I just saw a statistic that caused me dismay. There are 13 high schools in Baltimore. They had a zero understanding in math. Everyone failed the basic mathematics part of their qualifications. This is one of reasons I support Professor Leonard in his quest to get the knowledge out. We need to have proficiency in mathematics to continue becoming a place in the world where scholars come to learn. Are we really headed to an idiocracy in America?

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[@jeffcrain9757]

Spoiler Alert: wait until you discover Taylor polynomials in Cal 2. That alone got me very interested in Numerical Analysis. You can approximate any function with a polynomial! To be exact, a power series. Which is no more than a polynomial with powers of "x". Go back and watch the Cal 2 videos from Professor Leonard.

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@29:28 liked the video cause of the dance moves.

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when he says domain is all real numbers, is he referring to the power of the exponents ? Because polynomials can have complex roots

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Hii professor I completed your pre calculus and calculus 1 class and desperately want to complete calculus 2&3 but those are very lengthy and i have my exams in 4-5 months and 7 subjects to complete (mech engineering) please suggest me some books to get a basic idea of calculus and DE

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Do not care about polynomials, just watch Leonard

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Polynomials are very special in the "calculusy world". Polynomials are the first mathematical constructs you work with in calculus. I just learned the term "a calculusy idea" from Sean Carroll when talking about parallel transport of a vector in quantum field theory. Applying calculus produces a "tensor". Calculus is no more than just shrinking any curvy things down to where the curve becomes flat. Like standing on the earth anywhere in the desert. You don't see that the earth is round. All you see is flat. I think the ideas of calculus should be taught early. Precalculus is mainly a mechanics course. Sometimes I think it shouldn't even be a course in mathematics in college. But that's just me.

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Very detailed however do you have a basic video to explain what is co-efficient exponent real number

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Wait how come 0 is a polynomial function isn’t the domain- all real numbers(whole numbers) and 0 isn’t a whole number ????

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so what is the difference between POLYnomial and MONOmial?

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polynomials have multiple terms hence the prefix poly and mononomials only have one term hence the prefix mono

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