Algebraic expression

In mathematics, an algebraic expression is an expression that contains only algebraic numbers, variables and algebraic operations. Algebraic operations are addition, subtraction, multiplication, division and exponentiation with integral or fractional exponents. 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 $\sqrt{x + 4}$.

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 given n≥5 it can be done for some equations but not for others.

Reference

James, Robert Clarke; James, Glenn (1992). Mathematics dictionary. p. 8. 

External links

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