Coefficient
Numerical factor of a term
Coefficient refers to a numerical factor that is used in front of a variable or a constant in an algebraic expression. In mathematical equations or formulas, coefficients are essential to balance an equation or simplify an expression. Coefficients can be positive, negative, whole numbers, decimal numbers, or fractions.
For example, in the equation 2x + 3y = 12, the coefficients are 2 and 3, respectively, in front of the variables x and y, and 12 is called the constant term. The coefficients are used to determine the slope and the intercept of a linear equation.
In another example, if we have the quadratic equation y = ax² + bx + c, where a, b, and c are coefficients, the coefficient a determines whether the quadratic curve is concave up or down; if a is positive, the curve is concave up, while if a is negative, the curve is concave down.
In summary, coefficients play a critical role in algebraic equations and are used to simplify expressions, balance equations, find slope and intercept, determine characteristics of curves, and solve mathematical problems.
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