- published: 23 Oct 2015
- views: 137757
In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example in three variables is x3 + 2xyz2 − yz + 1.
Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.
According to the Oxford English Dictionary, polynomial succeeded the term binomial, and was made simply by replacing the Latin root bi- with the Greek poly-, which comes from the Greek word for many. The word polynomial was first used in the 17th century.
This video introduces students to polynomials and terms. Part of the Algebra Basics Series: https://www.youtube.com/watch?v=NybHckSEQBI&list;=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G Learn More at mathantics.com Visit http://www.mathantics.com for more Free math videos and additional subscription based content!
At the beginning of class, we make a pledge to stay positive and not let the math intimidate us. Well, it worked. We took that good energy and used it to solve polynomial equations of varying degrees. In a touching moment, the students said I'd be a good dad - wow - I love this work. YAY MATH! Please visit yaymath.org Videos copyright (c) Yay Math
If you can't get enough of Sal adding and subtracting polynomials, here's a bunch of many more examples. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/e/adding_and_subtracting_polynomials?utm_source=YT&utm;_medium=Desc&utm;_campaign=AlgebraII Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/v/multiplying-polynomials?utm_source=YT&utm;_medium=Desc&utm;_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/v/terms-coefficients-and-exponents-in-a-polynomial?utm_source=YT&utm;_medium=Desc&utm;_campaign=AlgebraII Algebra II on Khan Academy: Your studies in alg...
Polynomial Division Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/dividing_polynomials/v/polynomial-divided-by-monomial?utm_source=YT&utm;_medium=Desc&utm;_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/v/analyzing-polynomial-manipulations?utm_source=YT&utm;_medium=Desc&utm;_campaign=AlgebraII Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalitie...
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For a complete lesson on solving polynomial equations, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the first step in solving polynomial equations is to set the given equation equal to zero, the next step is to factor, and the final step is to set each of the resulting factors equal to zero and solve each equation. This process usually yields more than one solution, so the answer can be written as a solution set. Some of the problems involve factoring a trinomial into two binomials, and some of the problems involve factoring a binomial as the difference of two squares.
Please consider supporting me on Patreon! Be a Patron of Mathematics! https://www.patreon.com/patrickjmt?ty=h Thanks for watching and please subscribe! Visit PatrickJMT.com and 'like' it! :) Long Division of Polynomials - How to do long division on polynomials. 3 examples are shown! For more free math videos, visit http://PatrickJMT.com Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor
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How to Divide Polynomials with Long Division? - Long Division of Polynomials - Polynomial long division - Division of Polynomials. How to do Long Division with Polynomials of same degree? How to do Long Division with Binomials? Long Division with Polynomials with remainder? Explains how to do Long Division with polynomials step by step? Polynomials can sometimes be divided using the simple methods shown on Dividing Polynomials. But sometimes it is better to use "Long Division". Division of Polynomials - The Method: Write it down neatly: polynomial-long-division; the denominator goes first; then a ")"; then the numerator with a line above. Both polynomials should have the "higher order" terms first (those with the largest exponents, like the "2" in x2). Divide the first term of t...