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In mathematical logic, a "logical expression" can refer to either terms or formulas. A term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. A first-order term is recursively constructed from constant symbols, variables, and function symbols.
A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as x 2 + 4x + 4. An irrational algebraic expression is one that is not rational, such as √ x + 4.
A first-order term is recursively constructed from constant symbols, variables and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.
As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms. Such combination is called combining like terms or collecting like terms, and it is an important tool used for solving equations.
Such expressions of the solutions in terms of the parameters are also called solutions. A system of equations is a set of simultaneous equations , usually in several unknowns for which the common solutions are sought.
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
The number 3 is a constant term. [1] After like terms are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial + +, where is the variable, as having a constant term of .
Layers of Pascal's pyramid derived from coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial. In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials. [1]