# 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.