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Term Definition

A term in mathematics is a variable, constant, or the result of acting on variables and constants by function symbols. In simpler terms, terms are parts of an expression or series separated by addition or subtraction signs, or the parts of a sequence separated by commas. The word term is also used commonly to mean a summand of a polynomial including its coefficient (more properly called a monomial), or the corresponding quantity in a series (a series term).

Examples

Examples of expressions and their associated terms:

Expression

Terms

3a4 + 5xy - 1

3a4, 5xy, and 1

3k - 2t / x3 + y2

3k, 2t, x3, and y2

abc - def

abc, and def

x3y2 ÷ x2y

x3y2, and x2y

Dividing Terms

One term is said to divide another if the powers of its variables are no greater than the corresponding powers in the second monomial. For example, x2y divides x3y but does not divide xy3. A term m is said to reduce with respect to a polynomial if the leading term of that polynomial divides m. For example, x2y reduces with respect to 2xy + x + 3 because xy divides x2y, and the result of this reduction is x2y – x(2xy + x + 3)/2, or -x2/2 – 3x/2. A polynomial can therefore be reduced by reducing its terms beginning with the greatest and proceeding downward. Similarly, a polynomial can be reduced with respect to a set of polynomials by reducing in turn with respect to each element in that set. A polynomial is fully reduced if none of its terms can be reduced.

Related Definitions

Sources

“Term.” From Wolfram MathWorld, mathworld.wolfram.com/Term.html.

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