Maths Fa2 - Polynomials

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by chrisbliss
Last updated 5 years ago

Algebra I

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Maths Fa2 - Polynomials

Rings of polynomials in a finite number of variables are of fundamental importance in algebraic geometry which studies the simultaneous zero sets of several such multivariate polynomials. These rings can alternatively be constructed by repeating the construction of univariate polynomials with as coefficient ring another ring of polynomials: thus the ring R[X, Y] of polynomials in X and Y can be viewed as the ring (R[X])[Y] of polynomials in Y with as coefficients polynomials in X, or as the ring (R[Y])[X] of polynomials in X with as coefficients polynomials in Y. These identifications are compatible with arithmetic operations , but some notions such as degree or whether a polynomial is considered monic can change between these points of view. One can construct rings of polynomials in infinitely many indeterminates, but since polynomials are (finite) expressions, any individual polynomial can only contain finitely many indeterminates

Polynomials Today

1.(a+b)2 = a2 +2ab +b2 2. (a-b)2 = a2 -2ab+b2 3. (a+b) (a-b) = a2 -b2 4. (x+a)(x+b) = x2 + (a+b)x +ab 5. (x+a)(x-b) = x2 + (a-b)x -ab 6. (x-a)(x+b) = x2 + (b-a)x -ab 7. (x-a)(x-b) = x2 - (a+b)x + ab

Calculus - The simple structure of polynomial functions makes them quite useful in analyzing general functions using polynomial approximations.Abstract algebra - In abstract algebra, one distinguishes between polynomials and polynomial functions. A polynomial f in one indeterminate X over a ring R is defined as a formal expression of the form.Divisibility - In commutative algebra, one major focus of study is divisibility among polynomials. If R is an integral domain and f and g are polynomials in R[X], it is said that f divides g or f is a divisor of g if there exists a polynomial q in R[X] such that f q = g.

How it all BEGAN ??

In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining the number of positive or negative real roots of a polynomial.

Conclusions :

Polynomials have a lot of applications in day to day life. We all should learn and use the formulas to expend our learning. By Chris D'souzaGroup 2

Extensions of Polynomials


A video....

Rene Descartes


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