Page 115 - Start Up Mathematics_8 (Non CCE)

6 Algebraic Expressions and Identities:

Part II

In the previous chapter, we have learnt about addition, subtraction and multiplication of monomials, binomials
and trinomials. In this chapter, we will increase our knowledge on polynomials and division of algebraic
expressions.

Polynomial

A polynomial is an algebraic expression formed with constants, variables and exponents of the
variables can only be non-negaztive integers like 0, 1, 2, 3, etc. A polynomial cannot have infinite number of
terms.
3
2
For example, 5x – 7x + 8x – 1 is a polynomial.

–2
However, 5xy , x and 3 are not polynomials.
x 2+
The polynomials in one variable are called univariate polynomials. Similarly, polynomials with two or three
variables are called bivariate or trivariate polynomials, respectively.

Degree of polynomial in one variable
In a univariate polynomial, the highest power of the variable is called its degree.
For example, (a) 4x + 5 is a polynomial of degree 1.

4 7
2
(b) x - x + 6 is a polynomial of degree 2.
5 8
2
3
(c) 7x – 11x + 8x + 5 is a polynomial of degree 3.
Degree of polynomial in two variables
In a bivariate polynomial, the sum of the exponents of the variables in each term is calculated and the highest
sum is called the degree of the polynomial.

2
3
2
For example, (a) 4x y – 7xy + 3x + 5 is a polynomial in two variables x and y of degree 4.
3 1
2 2
2
(b) p - 6p q + p q - 7q + is a polynomial in two variables p and q of degree 6.
6
3 3
4 2
Constant polynomial
A polynomial consisting of only a constant term is called a constant polynomial.
For example, 3, –5, 6, –8 are constant polynomials. The degree of a constant polynomial is zero.

Linear polynomial

A polynomial of degree 1 is called a linear polynomial.
1
For example, x + 3, 2x – 7, x + 6 are linear polynomials.
4