Coefficient

A coefficient is the numerical factor multiplying a variable in an algebraic expression. In $5x^2 + 3x - 7$:

• Coefficient of $x^2$: $5$
• Coefficient of $x$: $3$
• Constant term: $-7$ (no variable; sometimes called the "constant coefficient")

When a variable appears without a visible number, the coefficient is 1 (or −1 if there's only a minus sign): $x^3 - x = 1 \cdot x^3 - 1 \cdot x$.

In multivariable expressions, the coefficient depends on which term we mean. In $4xy^2$, the coefficient of $xy^2$ is $4$, the coefficient of $y^2$ is $4x$, depending on what you treat as variable.

Coefficients are central to:

• Polynomial identification (degree from highest non-zero coefficient)
• Linear systems (the matrix of coefficients)
• Statistics (regression coefficients)
• Physics (coefficient of friction, drag, restitution).