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Last updated on September 16, 2025
In an algebraic expression, a coefficient is the numerical factor of the variable. It is typically a number, but a symbol representing a number can also act as a coefficient. For example, x is the variable and 2 is the coefficient in the expression, 2x².
Coefficient is the numerical factor multiplied by a variable in an expression. Some algebraic terms may not have any numerical value. In such cases, we assume the coefficient of the variables as 1.
For instance, the coefficient of x in the expression 3x is 3, but the coefficient of x² in the expression x² + 3 is 1. In the expression x² + 3, the variable x² is multiplied by 1, so its coefficient is 1.
Now that we know what a coefficient is, let's examine its role in an expression. It tells us the number of times the variable is multiplied.
For instance, the coefficient in the expression 7x is 7, indicating that x is being multiplied by 7. Likewise, the coefficient in the expression -3ab is -3, which means that the product of a and b will be multiplied by -3. The coefficient is interpreted as 1 or -1, when a variable appears without a number in front of it, as in x or -x. Coefficients are crucial in algebra because they assist in determining the value of expressions.
To determine the coefficient, always identify the numerical factor multiplying the variable. The number that multiplies the variable is the numerical coefficient. For example, the numerical coefficient in the expression 5 × x is 5.
In a polynomial, the leading coefficient refers to the coefficient of the term that has the highest power of the variable. For example, let us consider the polynomial 4x² + 3x - 7. Here, the term 4x² has the highest power of the variable x. So, its coefficient, 4, is the leading coefficient.
We can solve algebraic expressions more accurately and quickly if we are aware of certain tips and tricks. Here are a few tips that could be helpful while solving problems involving coefficients:
In real-world scenarios, coefficients are essential, particularly when working with quantities, rates, and patterns. Here are a few examples of real-world uses for coefficients along with brief descriptions:
Coefficients may seem like a tricky subject for those who are not familiar with the concept. Not understanding it thoroughly may lead to errors. However, we can avoid those errors if we practice regularly and pay attention to details. Mentioned below are some common mistakes that students make while working on coefficients.
What will be the Coefficient of x in the term 7x?
7
In the term 7x, the variable x is getting multiplied by the number 7. So, 7 is the coefficient.
Which coefficients are present in the formula 4a + 3b - 2c?
4, 3, and -2.
The coefficients of each variable are multiplied by a number: 4a has 4, 3b has 3, and -2c has -2.
Determine the coefficient of the term (3/4)m.
3/4
The coefficient is, 3/4 since the variable m is multiplied by the fraction 3/4.
What is the term 0z's coefficient?
0
The coefficient is zero since the variable z is multiplied by zero. Regardless of z's value, the entire term becomes 0.
Determine the coefficients in the following expression: 2xy – 5yz + z
2, -5, and 1.
The numbers that appear before each variable term are the coefficients. Its coefficient is 1 if there is no number before z. The coefficients are 2 (for xy), -5 (for yz), and 1 (for z).
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.