Page 138 - ICSE Math 8

Coefficient

Any factor of a term is known as the coefficient of the product of the remaining factors. For example,
2
2
2
(a) In the term 9ab , 9 is the coefficient of ab , a is the coefficient of 9b , and so on.
2
2 2
2
2 2
(b) In the term –3x y , –3 is the coefficient of x y , x is the coefficient of –3y , and so on.
If the factor is a constant, it is called a numerical coefficient. The factor involving literals is known as a literal
coefficient.
Algebraic Expression
A single term or a combination of two or more terms connected by plus (+) or minus (–) signs is known as an
algebraic expression. For example, b b
(a) In the algebraic expression 3xy + 4 , there are two terms namely, 3xy and 4 .
a
a
3
(b) In the algebraic expression 7ab , there is only one term.
(c) In the algebraic expression 3a + 4b + 5ab, there are three terms namely, 3a, 4b and 5ab.
There are different types of algebraic expressions based on the number of terms.

Monomial
An algebraic expression which contains only one term with non-negative integral powers of variables is known
as a monomial. For example, ab, 7b and 4xz are monomials.
Binomial
An algebraic expression containing exactly two terms with non-negative integral powers of variables is known
3
2
2
as a binomial. For example, 3xy + 4b and 9b + 4a are binomials.
Trinomial
An algebraic expression which contains three terms with non-negative integral powers of variables is known
3
as a trinomial. For example, 7a + b + xyz and 3bz + 4 + 9zc are trinomials.
Polynomial in One Variable
An algebraic expression in which the exponents of a variable are non-
negative integers is called a polynomial in one variable. A polynomial in one Maths Info
1 1 1
variable say x, cannot have terms such as , and . So, we can say that A polynomial consisting of only
x
2
3
x
x
a constant term is known as a
n
a polynomial in x can only have terms of the form ax , where a is a constant constant polynomial.
5
3
2
and n is a non-negative integer. For example, 4x – 3x + 1 and 9x – x are
polynomials in x. 3
Polynomial in Two or More Variables
An algebraic expression in which the exponents of two or more variables are non-negative integers is called
a polynomial in two or more variables. For example,
2
3
(a) 5x – 2xy + 3xy – y is a polynomial in two variables x and y.
3
2
(b) 8ab + 3b – 5a c is a polynomial in three variables a, b and c.
Degree of a Polynomial
The degree of a polynomial in one variable is the highest power of the Maths Info
variable. For example,
5
3
(a) 8x + 7x – 5 is a polynomial in x with degree 5. A constant is a polynomial of
4
3
(b) –3x + x + 4x is a polynomial in x with degree 4. degree 0.
(c) –18 is a constant polynomial with degree 0.
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