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define algebraic expression
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An algebraic expression is a mathematical phrase made from numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division, and often exponentiation and root extraction), but not including an equals sign. It represents a quantity, not a statement.
Key parts
- Terms: pieces added or subtracted (e.g., 3x^2, −5xy).
- Coefficients: numerical factors of terms (3 in 3x^2).
- Variables: symbols that stand for numbers (x, y).
- Degree: the highest power of the variable(s) in a polynomial term.
Examples
- 3x^2 − 5xy + 7 (polynomial)
- (x + 1)/(x − 2) (rational expression)
- √(x + 2) (in many contexts treated as algebraic because it uses a root)
Non-examples
- x + 2 = 5 (an equation, not an expression)
- sin x, e^x (transcendental functions — not algebraic in the strict sense)
Types commonly referenced: monomial, binomial, trinomial, polynomial, and rational expression.
Key parts
- Terms: pieces added or subtracted (e.g., 3x^2, −5xy).
- Coefficients: numerical factors of terms (3 in 3x^2).
- Variables: symbols that stand for numbers (x, y).
- Degree: the highest power of the variable(s) in a polynomial term.
Examples
- 3x^2 − 5xy + 7 (polynomial)
- (x + 1)/(x − 2) (rational expression)
- √(x + 2) (in many contexts treated as algebraic because it uses a root)
Non-examples
- x + 2 = 5 (an equation, not an expression)
- sin x, e^x (transcendental functions — not algebraic in the strict sense)
Types commonly referenced: monomial, binomial, trinomial, polynomial, and rational expression.
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