In mathematics, a coefficient is a numerical or constant factor multiplied by a variable or variables in an algebraic expression or equation. Coefficients quantify the relationship between different terms in an equation or expression.
In a polynomial equation, the coefficients are the numbers multiplied by the different powers of the variable. For example, in equation 2x^2 + 5x - 3, the coefficient of the x^2 term is 2, the coefficient of the x term is 5, and the coefficient of the constant term is -3.
Coefficients can also be used to represent the relationship between variables in a linear equation. For example, in the equation y = mx + b, where m and b are coefficients, m is the slope of the line and b represents the y-intercept.
Coefficients are critical to algebraic manipulations, solving equations, and understanding mathematical expressions and equations. They provide information about the relative magnitude, direction, and interaction of the variables involved.