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What Does Coefficient Mean in Math?

July 31, 2022
written by Azhar Ejaz

In mathematics, a coefficient is a number or quantity representing a constant value that is multiplied by the variable. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and ‘a’ and ‘b’ are the coefficients.

What is a coefficient?

The coefficient is “Any number with we multiply a variable.” For example, in the term 5x, 5 is the coefficient of the variable x, and in -6z, -6 is the coefficient z. In other words, a coefficient is a multiplicative factor in the terms of, a series, polynomial, or any expression. Observe the following expression which shows that 7 is the coefficient of x2 and 5 is the coefficient of y.

image showing the coefficient

A coefficient can be negative or positive, imaginary, or real in the form of fractions or decimals.

What is the Coefficient of a Variable?

The coefficient of a variable is the value of the integer or any letter that is multiplied by the variable. For example, the coefficient of variable x in the expression 3x + 5y is 3, and in the expression 4x+7y the coefficient of variable y is 7. The coefficient of the variable x2 in the standard form of quadratic equation ax2 + bx + c is a.

What is the Coefficient of a Variable?

 A numerical coefficient is a number that is the multiplying of the variables in a term. For example, 4 is the numerical coefficient of the term 4mn. The term numerical coefficient is used for the constant multipliers of the variable. An example is 6xy. Here, the numerical coefficient of xy is 6.

What is Leading Coefficient?

The coefficient of the term with the greatest power of the variable in an expression is called the leading coefficient. In other words, when writing the polynomial in its standard form, the Coefficient of the first term of the variable is called the leading coefficient.

image showing the leading coefficient

For example:

PolynomialStandard formLeading coefficient
5x-2x2-3x3-3x3-2x2+5x -3


  • A coefficient is always multiplied by a variable.
  • A variable, not a number has 1 as its coefficient.
  • We cannot have zero (0) as the coefficient, as the value of the term with zero as the coefficient is zero.
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