Algebraic expression

In mathematics, an algebraic expression is an expression that contains variables and a finite number of algebraic operations (addition, subtraction, multiplication, division and exponentiation to a rational exponent). A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as x² + 2x + 4. An irrational algebraic expression is one that is not rational, such as √x + 4.

Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression with a finite number of operations involving just those coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or four; but for degree five or more it can only be done for some equations but not for all.

See also

• Analytical expression

References

• Morris, Christopher G. (1992). Academic Press dictionary of science and technology. p. 74. http://books.google.co.uk/books?id=nauWlPTBcjIC&lpg=PA74&dq=algebraic%20expression%20over%20a%20field&pg=PA74#v=onepage&q&f=false. 
• James, Robert Clarke; James, Glenn (1992). Mathematics dictionary. p. 8. http://books.google.co.uk/books?id=UyIfgBIwLMQC&lpg=PA8&dq=algebraic%20expression%20over%20a%20field&pg=PA8#v=onepage&q&f=false. 

External links

• Weisstein, Eric W., "Algebraic Expression" from MathWorld.