An algebraic Expressions is an expression formed from any combination of numbers and variables by using the operations of addition, subtraction, multiplication, division, exponentiation (raising to powers), or extraction of roots.
For instance,,, , , , and are algebraic expressions. By an algebraic expression in certain variables, we mean an expression that contains only those variables, and by a constant, we mean an algebraic expression that contains no variables at all. If numbers are substituted for the variables in an algebraic expression, the resulting number is called the value of the expression for these values of the variables.
If an algebraic expression consists of parts connected by plus or minus signs, it is called an algebraic sum, and each parts, together with the sign preceding it, is called a term. For instance, in the algebraic sum
An algebraic expression such as can be considered an algebraic sum consisting of just one term. Such a one-termed expression is called a monomial. An algebraic sum with two terms is called a binomial, and an algebraic sum with three terms is called a trinomial. For instance, the expression is a binomial, whereas is a trinomial. An algebraic sum with two or more terms is called a multinomial.
A polynomial is an algebraic sum, in which no variables appear in denominators or under radical signs, and all variables that do appear are raised only to positive-integer powers. For instance, the trinomial is not a polynomial; however, the trinomial is a polynomial in the variables and. A term such as , which contains no variables, is called a constant term of the polynomial. The numerical coefficients of the terms in a polynomial are called the coefficients of the polynomial. The coefficients of the polynomial above are , , and .
A polynomial of degree in a single variable can be written in general form