coefficient

coefficient — noun

1. In algebra, a number or symbol that is written before a variable and tells you h

1.名詞B2
釋義

In algebra, a number or symbol that is written before a variable and tells you how many times that variable is included in a term. For instance, in the expression 4y, the coefficient 4 shows that y is taken four times.

例句

In the equation 5x + 3 = 18, the coefficient of x is the number 5.

coefficient of [variable] before an equals sign

Theo noticed that the term 9b² has a coefficient of 9.

coefficient in a squared term

同義詞
  • multiplier

    Emphasises the multiplying function; less common in classroom algebra, more used in statistics and economics.

  • factor

    Broader term — any number that divides into or combines with others; not specific to the number in front of a variable.

  • numerical factor

    Formal phrasing; used in textbooks to distinguish the number from the variable part of a term.

文法句型

coefficient of [variable]

用法筆記

Often appears with 'of' followed by the variable: ‘the coefficient of x’. A variable with no written number has an implied coefficient of 1.

常見錯誤

❌The number 3 in 3× is called a constant.
✅The number 3 in 3x is called a coefficient.
💡A constant stands alone (like the 5 in x + 5), while a coefficient multiplies a variable.
❌The coefficient of x in x² + 2x is 2.
✅The coefficient of x² is 1 and the coefficient of x is 2.
💡Each power of a variable has its own coefficient.

2. A number used in science and engineering to express how much of a specific physi

2.名詞B2
釋義

A number used in science and engineering to express how much of a specific physical property a material or system has. Examples include the coefficient of friction between two surfaces and the coefficient of thermal expansion of a metal.

例句

The friction coefficient between rubber tyres and dry asphalt is roughly 0.9.

friction coefficient + material pair

Engineers calculated the thermal expansion coefficient of steel before building the railway track.

同義詞
  • index

    Used in specific fields like optics (refractive index); narrower in meaning.

  • constant

    A value that stays fixed under given conditions; a coefficient is one type of constant.

  • modulus

    Refers specifically to a measure of a physical property such as elasticity; more technical than coefficient.

文法句型

coefficient of [property]

[property] coefficient

用法筆記

Most commonly appears in compound terms such as 'friction coefficient' or 'coefficient of expansion'. Each scientific field has its own specific coefficients with standard symbols.

常見錯誤

❌The rate of friction is 0.5.
✅The coefficient of friction is 0.5.
💡'Coefficient' refers to a fixed measure of a property, not a rate of change.