Coefficient

Definition

A coefficient is a numerical or constant factor that multiplies a variable in an algebraic expression. For example, in the term $3x^2$, 3 is the coefficient.

5 Must Know Facts For Your Next Test

1. A coefficient can be positive, negative, or zero.
2. In polynomial functions, coefficients are associated with each power of the variable.
3. The leading coefficient is the coefficient of the term with the highest degree.
4. Changing a coefficient alters the steepness and direction of a graph but not its basic shape.
5. In rational expressions, coefficients appear in both the numerator and denominator.

Review Questions

• What is the coefficient in the term $7x^3$?
• How does changing the leading coefficient affect a polynomial's graph?
• In the polynomial $4x^4 + 3x^3 - 2x + 5$, what are the coefficients?

Related terms

Polynomial: An algebraic expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.

Leading Coefficient: The coefficient of the term with the highest degree in a polynomial.

Constant Term: A term in an algebraic expression that does not contain any variables; it has a fixed value.