Algebraic Expressions & Polynomials

Algebraic Expressions

Expressions, involving arithmetical numbers, variables and symbols of operations are called algebraic expressions. An algebraic expression is a combination of numbers, variables and arithmetical operations.

Term of Expression

One or more signs + or – separates an algebraic expression into several parts. Each part along with its sign is called a term of the expression.

Polynomial

An algebraic expression, in which variables do not occur in the denominator, exponents of variables are whole numbers and numerical coefficients of various terms are real numbers, is called a polynomial.

In other words,

  • No term of a polynomial has a variable in the denominator.
  • In each term of a polynomial, the exponents of the variables are non-negative integers.
  • Numerical coefficient of each term is a real number.

x2 + 8 is a polynomial in one variable x and 2x2 + y3 is a polynomial in two variables x and y.

General form of a polynomial in one variable x is:

a0 + a1x + a2x2 + ....+ anxn

where coefficients a0, a1, a2, ....an are real numbers, x is a variable and n is a whole number. a0, a1x, a2x2, ...., anxn are (n + 1) terms of the polynomial.

An algebraic expression or a polynomial, consisting of only one term, is called a monomial. An algebraic expression or a polynomial, consisting of only two terms, is called a binomial. An algebraic expression or a polynomial, consisting of only three terms, is called a trinomial.

The terms of a polynomial, having the same variables and the same exponents of the variables, are called like terms. Terms that are not like, are called unlike terms.

For example, in the expression: 3xy + 9x + 8xy – 7x + 2x2

The terms 3xy and 8xy are like terms. Also 9x and –7x are like terms.