At the conclusion of this project, you will have learned the background of how the process of multiplying, substracting, dividing, additioning polynomials came about, understood the language used, and presented multiple methods to complete the process depending on the problem given. You will have discovered when this math is utilized and how important it is to understand for professions in the real world. You learned the usage of the techniques and how to sketch a polynomial's graph with the help of the videos.differently next time as a group. You should be able to successful complete the process of operating polynomials yourself and explain to anyone, why it is important and when it would be beneficial to know.
1 Get all the terms on the same side. Before you can solve a polynomial equation, you have zero on one side of the equation and everything else on the other. Fortunately, you can use addition or
subtraction to move things around. For example, if you have the equation x^2 + 2x = 8, you can subtract 8 from both sides: x^2 +2x = 8x^2 + 2x -8 = 8 -8x^2 +2x -8 = 0
2 Factor out any number you can. If a number is a factor of all the terms in the equation, you can factor it out. For example, in 4y^2 +8y + 6 = 0 , 2 is a factor of everything, since all three terms on the left side can be divided by two. Factoring it out, we get: 4y^2 8y +6 = 02(2y^2 + 4y +3) = 0
3 Factor out any common variables. If every term in your polynomial has a variable in it, you can factor it out just like a number. For example, in the polynomial 3a^2 +a = 0 , both terms have an "a" in them: 3a^2 +a = 0a(3a +1) = 0
4 Factor any remaining complex terms. For example, once you factor out the number "2" from 2x^2 - 2 = 0, you are left with 2(x^2 -1) = 0. You can factor this one step further: 2(x^2 -1) = 02(x+1)(x - 1) = 0 See the link below to learn more about factoring polynomials.
5 Solve the equation. Once the left side is factored out, you can get a solution by noticing that every part with a variable is equal to zero. For example, in 2(x + 1)(x - 1) = 0, both x + 1 and x - 1 are equal to zero. You can get two solutions by just plugging in the numbers:First Solutionx + 1 = 0x + 1 - 1 = 0 - 1x = -1 Second Solution x - 1 = 0 x - 1 + 1 = 0 + 1x = 1
Polynomial comes from the Greek poly, "many" and medieval Latin binomium, "binomial". The word was introduced in Latin by Franciscus Vieta.
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 toeconomics 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, a central concept in abstract algebra and algebraic geometry.
Polynomials can be used to model different situations, like in the stock market to see how prices will vary over time, in physics to describe the trajectory of projectiles and in industry. Polynomial integrals can be used to express energy, inertia and voltage difference, to name a few applications. In this webquest, you will discover the operations of polynomials.
