polynoomses

A polynoom is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynoom in a single indeterminate x is commonly written as a sum of terms, each term being the product of a coefficient and a non-negative integer power of x. For example, 3x^2 - 5x + 2 is a polynoom. The highest power of the variable in a polynoom is called its degree. In the example 3x^2 - 5x + 2, the degree is 2.

Polynoms can have one or more variables. A polynoom in two variables, say x and y, might look like 2x^2y + 3xy - 5y^3. The degree of a term in a multi-variable polynoom is the sum of the exponents of the variables in that term. For 2x^2y, the degree is 2+1=3. The degree of the entire polynoom is the highest degree of any of its terms.

The coefficients of a polynoom are typically numbers, but can also be elements of a ring or field. When the coefficients are integers, the polynoom is called an integer polynoom. If the coefficients are real numbers, it's a real polynoom, and if they are complex numbers, it's a complex polynoom.

Polynoms are fundamental in algebra and have applications in various fields, including calculus, number theory, and computer science. They are used to approximate functions, solve equations, and model real-world phenomena. The study of polynoms includes their factorization, roots, and graphical representations.