polynomické

Polynomické is an adjective in Czech and Slovak mathematics meaning “polynomial” or “related to polynomials.” A polynomial P(x) is an expression of the form a0 + a1 x + a2 x^2 + ... + an x^n, where the coefficients ai come from a field or ring and n is a nonnegative integer. The degree of P is the largest i with ai ≠ 0. Monomials are single-term polynomials ai x^i.

Polynomials can be added, subtracted, and multiplied; division by a nonzero polynomial yields a quotient and remainder (polynomial long division). Over a given field, a polynomial is reducible if it can be factored into polynomials of smaller degree; otherwise it is irreducible. Over the complex numbers, every nonconstant polynomial splits into linear factors.

Polynomial functions are functions defined by polynomials: f(x) = a0 + a1 x + ... + an x^n. They are continuous and differentiable, with the derivative f'(x) having degree n-1 (if n ≥ 1). Polynomials are used in interpolation and approximation, such as polynomial interpolation (Lagrange, Newton) and polynomial regression, and they appear in numerical methods and modeling.

Origin and usage: the term polynomické derives from Greek poly “many” and onoma “name.” In Czech and Slovak, polynomické describes polynomial-related objects, including polynomické rovnice (polynomial equations) and polynomické funkce (polynomial functions).