Meaning & use
coefficient
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Meanings
nouncountablemathematics
A number written in front of a variable that tells you how many times that variable is taken, as the 5 in 5x.
Grammar: Usually followed by of: the coefficient of x.
Patterns
- the coefficient of something
- a coefficient for something
In the expression 7y + 2, the coefficient of y is 7.
Students must find the coefficient of x squared before they can solve the equation.
If the leading coefficient is negative, the parabola opens downward.
nouncountablephysicstechnical
A fixed number or ratio that measures how strongly a property or relationship appears, such as how much a material expands when heated.
Grammar: Often part of a compound: the coefficient of friction.
Patterns
- the coefficient of something
- a correlation coefficient
The coefficient of friction between rubber and wet ice is very low.
Engineers checked the thermal expansion coefficient of the steel before building the bridge.
A correlation coefficient close to 1 suggests the two measurements move together.
Word forms
| plural | coefficients |
|---|
Common combinations
- correlation coefficient
- The correlation coefficient between study time and grades was 0.8.
- leading coefficient
- The leading coefficient of the polynomial is 3.
- coefficient of friction
- A higher coefficient of friction means the tires grip better.
- numerical coefficient
- Remove the variable and you are left with the numerical coefficient.
- determine the coefficient
- We determined the coefficient by repeating the experiment ten times.
Synonyms and how they differ
- factor
- Factor is a much broader word for anything that multiplies or influences a result, while coefficient names the specific constant attached to a variable or property.
- multiplier
- Multiplier stresses the act of scaling something up and is used in everyday contexts, whereas coefficient is the precise technical term in algebra and science.
- constant
- A constant is any fixed value, but a coefficient is specifically one tied to a variable or a measured relationship.
Word family
- co-efficiency noun
- rare word for combined efficiency, not used in math
- efficient adjective
- working well without waste, sharing the Latin root of effect
- coefficients noun
- the plural form used for several such numbers
Commonly confused: coefficient or constant?
coefficient vs constant
A constant is a fixed number on its own, such as 9 in x + 9, whereas a coefficient multiplies a variable.
Practice
In the expression 12x + 5, which number is the coefficient of x?
Choose one answer.
The coefficient is the number multiplying the variable, so 12 is correct. The 5 is a constant term, which is the tempting wrong choice.
Make it your own
Write a sentence using “coefficient”, then check it and compare it with the examples above.