What Is a Coefficient?
A coefficient is the number multiplied by a variable.
In 3x, the coefficient is 3. It means 3 × x.
In 7y, the coefficient is 7.
In x (by itself), the coefficient is 1 (because x means 1 × x).
In -2n, the coefficient is -2.
Why coefficients matter
Coefficients tell you "how many" of a variable you have:
- 3x means "3 of x" (like 3 apples)
- 5x means "5 of x"
- 3x + 5x = 8x (combine like terms, 3 of something plus 5 of something = 8 of something)
In equations
In the equation 3x = 21:
- The coefficient is 3
- To solve, divide both sides by the coefficient: x = 21 ÷ 3 = 7
In y = 2x + 5 (linear equation):
- The coefficient of x is 2 (the slope)
- The 5 is a constant (not a coefficient because it has no variable)
Common confusion
Confusing coefficients with exponents: In 3x², the 3 is the coefficient and the 2 is the exponent. They do different things: the coefficient multiplies, the exponent raises to a power.
Forgetting the coefficient of 1: x means 1x. When combining like terms, x + 3x = 4x (the invisible 1 matters).
Related concepts
- Variables: what coefficients multiply
- Equations and expressions: where coefficients appear
- Linear equations: the coefficient of x is the slope