Coefficient

Definition

A coefficient is a numerical or constant factor that multiplies a variable in a term of an algebraic expression or equation. For example, in the term $5x^2$, 5 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 determine the shape and position of the graph.
3. The leading coefficient is the coefficient of the term with the highest degree in a polynomial.
4. In a polynomial like $3x^3 + 2x^2 - x + 7$, 3, 2, -1, and 7 are all coefficients.
5. Coefficients can also be fractions or irrational numbers.

Review Questions

• What is the coefficient of $x$ in the term $-4x$?
• In the polynomial $6x^4 - 3x^2 + x - 8$, what is the leading coefficient?
• How do coefficients affect the shape of a polynomial's graph?

Related terms

Polynomial: An algebraic expression consisting of terms which are sums and/or differences of variables raised to non-negative integer powers and multiplied by coefficients.

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

Zero of a Polynomial: A value for which a given polynomial evaluates to zero; also known as root or solution.