In mathematics, a **polynomial** is an expression consisting of variables (or indeterminates) and coefficients that involves only addition, subtraction and multiplication and non-negative integer exponents. An example of a polynomial of a single variable or indeterminate, $ x $, would be $ x^2-4x+7 $ which is a Quadratic Polynomial.

Polynomials appear widely in Mathematics and Science. For example, Polynomials are used to form **Polynomial Equations**, which encode a wide range of problems, from elementary word problems to advanced problems in the sciences. They are also used to define **Polynomial Functions**, whih are used in advanced areas of Physics and Chemistry as well as Social Science and even Calculus. In advanced math, Polynomials are used for Advanced Algebra and Algebraic Geometry.

## Arithmetic of Polynomials Edit

Polynomials may be added according to the associative law of addition (grouping all their terms into a single sum), possibly followed by reordering and combining like terms. For example if

$ P=3x^2-2x+5xy-2 $

$ Q=-3x^2+3x+4y^2+8 $

then

$ P+Q=3x^2-2x+5xy-2-3x^2+3x+4y^2+8 $

which can be simplified to

$ P+Q=x+5xy+4y^2+6 $

To work out the product of Polynomials into a sum of terms, the Distributive Property is constantly applied, which results in one term of each Polynomial being multiplied by every term of the other. For example if

$ P=2x+3y+5 $

$ Q=2x+5y+xy+1 $