együtthatói

"Együtthatói" is a Hungarian word that translates to "coefficients" in English. In mathematics, coefficients are numerical or symbolic factors that multiply a variable in an algebraic term. For example, in the expression 5x², the number 5 is the coefficient of the variable x². Coefficients can be integers, fractions, decimals, or even other variables or expressions. They play a crucial role in defining the value and behavior of mathematical expressions and equations.

In the context of polynomials, coefficients are the numbers that precede the powers of a variable. For instance, in the polynomial 3x³ - 2x + 7, the coefficients are 3, -2, and 7. The coefficient of x² is implicitly 0, as it is not explicitly written. The constant term, like 7 in this example, is also considered a coefficient (specifically, the coefficient of x⁰).

Beyond basic algebra, coefficients are fundamental in various branches of mathematics and science. They appear in differential equations, linear algebra (as entries in matrices), physics (representing physical quantities like mass or force), chemistry (stoichiometric coefficients in chemical reactions), and engineering. The value and nature of coefficients often determine the properties and outcomes of the systems they describe. Understanding coefficients is therefore essential for comprehending and manipulating mathematical models and scientific principles.