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Algebra Connections Glossary
factor   
  (1) In arithmetic: When two or more integers are multiplied, each of the integers is a factor of the product.  For example, 4 is a factor of 24, because 4 · 6 = 24.   (2) In algebra: When two or more algebraic expressions are multiplied together, each of the expressions is a factor of the product.  For example, x² is a factor of −17x²y³, because (x²)(−17y³) = −17x²y³.   (3) To factor an expression is to write it as a product.  For example, the factored form of x² − 3x + 18 is
(x − 6)(x + 3).
factored completely   
  A polynomial is factored completely if none of the resulting factors can be factored further using integer coefficients.  For example,
−2(x + 3)(x − 1) is the completely factored form of −2x² − 3x + 6.
factored form    
  A quadratic equation in the form a(x + b)(x + c) = 0, where a is nonzero, is said to be in factored form.  For example, −7(x + 2)(x − 1.5) = 0 is a quadratic equation in factored form.
Fibonacci Sequence
  The sequence of numbers 1, 1, 2, 3, 5, 8, 13, …. Each term of the Fibonacci sequence (after the first two terms) is the sum of the two preceding terms.
Figure 0   
  The figure that comes before Figure 1 in a tile pattern.  When representing a tile pattern with a graph, the y-intercept of the graph is the number of tiles in Figure 0.  When representing a tile pattern with an equation in y = mx + b form, b gives the number of tiles in Figure 0.
F.O.I.L.   
  An approach for multiplying two binomials.  “F.O.I.L.” stands for “First, Outer, Inner, Last.”  It describes the order in which to multiply the terms of two binomials to be sure to get all the products.  For example, the equation below shows how to apply the F.O.I.L. method to multiply (2x + 3)(x - 4).

pic
fraction buster   
  “Fraction busting” is a method of simplifying equations involving fractions that uses the Multiplicative Property of Equality to rearrange the equation so that no fractions remain.  To use this method, multiply both sides of an equation by the common denominator of all the fractions in the equation.  The result will be an equivalent equation with no fractions.  For example, when given the equation pic, we can multiply both sides by the “fraction buster” 21.  The resulting equation, 3x + 42 = 7x, is equivalent to the original but contains no fractions.
function   
  A relation in which for each input value there is one and only one output value.  For example, the relation f(x) = x + 4 is a function; for each input value (x) there is exactly one output value.  In terms of ordered pairs (x, y), no two ordered pairs of a function have the same first member (x).
function notation   
  When a rule expressing a function is written using function notation, the function is given a name, most commonly “f,” “g,” or “h.”  The notation f(x) represents the output of a function, named f, when x is the input.  It is pronounced “f of x.”  For example, g(2), pronounced “g of 2”, represents the output of the function g when x = 2.  If g(x) = x² + 3, then g(2) = 7.