polinomosztás

Polinomosztás is the Hungarian term for polynomial division. It is a mathematical algorithm for dividing one polynomial by another polynomial of lesser or equal degree. The process is analogous to long division for integers. The goal is to find a quotient polynomial and a remainder polynomial. The remainder's degree must be strictly less than the degree of the divisor polynomial.

The algorithm involves repeatedly dividing the leading term of the dividend by the leading term of the divisor. This result becomes the next term in the quotient. This term is then multiplied by the entire divisor, and the result is subtracted from the dividend. The process is then repeated with the new polynomial obtained from the subtraction. This continues until the degree of the resulting polynomial is less than the degree of the divisor.

The fundamental theorem of algebra provides a theoretical basis for polynomial division, stating that any polynomial with complex coefficients can be factored into linear factors. Polynomial division is a crucial tool in algebra, used for tasks such as factoring polynomials, finding roots of polynomials, and simplifying rational expressions. It is a foundational concept in abstract algebra and has applications in various fields of mathematics and science.