polynoms

Polynomials are expressions consisting of variables (also called indeterminates) and coefficients, that involve only the operations of addition, subtraction, and multiplication, and non-negative integer exponents of variables. A polynomial is a sum of terms, each of which is a product of a coefficient and a variable raised to a non-negative integer power. For example, 3x^2 + 2x + 1 is a polynomial in the variable x.

The degree of a polynomial is the highest degree of any term in the polynomial. The degree of a term is the sum of the exponents of the variables in that term. For example, the degree of the polynomial 3x^2 + 2x + 1 is 2, because the highest degree term is 3x^2.

Polynomials can be classified based on their degree. A polynomial of degree 1 is called a linear polynomial, a polynomial of degree 2 is called a quadratic polynomial, and a polynomial of degree 3 is called a cubic polynomial. Polynomials of degree 4 or higher are called higher-degree polynomials.

Polynomials can be added, subtracted, and multiplied, and they can be divided by other polynomials to give a quotient and a remainder. The Fundamental Theorem of Algebra states that every non-constant polynomial with complex coefficients has at least one complex root. This means that a polynomial of degree n has exactly n roots, counting multiplicity.

Polynomials are widely used in mathematics and its applications, including algebra, calculus, and number theory. They are also used in computer science, engineering, and physics.