Polynomials

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
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

$$P=2x+3y+5$$

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