what is a coefficient
Algebraic expressions of Class 8
Each term in an algebraic expression is a product of one or more number(s) and / or literal number(s). These number(s) and / or literal number(s) are known as the factors of that term. For example:
The monomial 7x is the product of number 7 and literal x. So, 7 and x are factors of the monomial 7x.
In the binomial and are two terms. In the tem for instance, 3, x and y are its factors. Clearly, number 3 is the numerical factor, and x and y are literal factors.
In the term - the numerical factor is – 4 whereas x, yand z are literal factors.
In the binomial expression the term has −1 as the numerical factor while x and y are literal factors. The term 3 has only numerical factor. It has no literal factor.
In the algebraic expression the term ab has numerical factor as 1 and literal factors are a and b. The term has numerical factor as −1 and literal factors are c and The third term −7 has no literal factor.
In a term of an algebraic expression, any of the factors with the sign of the term is called the coefficient of the product of the other factors.
A term of the expression having no literal factor is called a constant term. For example:
In the binomial expression the constant term is 7.
In the trinomial expression the constant term is
Like terms and unlike terms:
The terms having the same literal factors are called the like terms other wise they are known as unlike terms.
In the expressions 2xy + 3x – 7xy + 5x, (2xy, – 7xy) and (3x, 5x) are like terms [have same literals factors]
3x, – 7xy are unlike terms [do not have same literal factors]
When a polynomial is written in its normal form, then the coefficient of the term containing the degree or the coefficient written with the primary term is known as leading coefficient. In other words, it's the coefficient of the term with the highest power in an expression.
Tips and Tricks on Coefficient
Keep the subsequent points in mind while working with coefficients:
- A coefficient is usually attached to a variable.
- A variable without a number has 1 as its coefficient.
- We cannot have 0 as the coefficient because the value of the term with 0 as the coefficient is 0.