The LessonA coefficient is a number that is placed in front of a variable. The coefficient is multiplying the variable.
Dictionary DefinitionThe Oxford English Dictionary defines a coefficient as "a number or quantity placed (usually) before and multiplying another quantity known or unknown."
Real Examples of CoefficientsIt is easier to understand coefficients with examples.
Consider the term below:
6 is the coefficient of x.
Consider the expression below. One of the coefficients is a letter rather than a number:
a (a constant) is the coefficient of x2. 1 is the coefficient of x, even though no number or letter is written in front of it (see Note). 2 is the coefficient of y.
Understanding CoefficientsThink of a letter in algebra as an object. We can count the objects. x is one x. If we add one x to one x, we get two x's.
x + x = 2xThe coefficient of 2 is telling us we have 2 x's. Another way of saying this is that the 2 is multiplying the x after it:
2x = 2 × x = x + xIf there was a coefficient of 3 in front of an x, we would have 3 x's:
3x = 3 × x = x + x + x
Letters As CoefficientsLetters can be used as coefficients. For example, a standard linear equation is y = mx + c. The m is the coefficient of the x term.
The letter still represents a number. The m could be a 2 or a −3 for different linear equations.
Lesson SlidesThe slider below has some more real examples of coefficients. Open the slider in a new tab
A Term Without a Number in Front of it Has a Coefficient of 1Sometimes a term will not have a number in front of it.
Don't be fooled. It still has a coefficient. The coefficient is 1.