Polünoomilisi

Polünoomilisi, commonly referred to as polynomials, are fundamental algebraic expressions. A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The general form of a polynomial in a single variable, say x, is given by $a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0$, where $a_n, a_{n-1}, ..., a_1, a_0$ are coefficients (which can be real numbers, complex numbers, or elements of other rings) and n is a non-negative integer representing the degree of the polynomial.

The terms of a polynomial are separated by addition or subtraction. Each term consists of a coefficient multiplied by one or more variables raised to non-negative integer powers. For example, $3x^2 - 5x + 2$ is a polynomial where 3, -5, and 2 are coefficients, and x is the variable. The highest power of the variable in a polynomial is called its degree. In the example $3x^2 - 5x + 2$, the degree is 2.

Polynomials can have one or more variables. A polynomial with one variable is called a univariate polynomial, while a polynomial with two or more variables is called a multivariate polynomial. Examples of polynomials include constants (degree 0), linear polynomials (degree 1, like $2x + 1$), quadratic polynomials (degree 2, like $x^2 - 4$), cubic polynomials (degree 3), and so on. They play a crucial role in various branches of mathematics, including algebra, calculus, and number theory, as well as in fields like physics, engineering, and economics.