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Factoring Trinomials of the Form x² + bx + c definitions

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  • Trinomial
    An algebraic expression with three terms, typically including a squared term, a linear term, and a constant.
  • Binomial
    An algebraic expression with two terms, often used as factors when breaking down trinomials.
  • Coefficient
    A numerical factor that multiplies a variable in an algebraic expression, such as the number before x or x².
  • Constant
    A fixed value in an expression that does not contain a variable, often represented as c in trinomials.
  • Factor Pair
    Two numbers whose product equals a given constant and whose sum matches another specified value.
  • FOIL Method
    A technique for multiplying two binomials by combining First, Outside, Inside, and Last terms.
  • Distributive Property
    A rule that allows multiplication to be distributed over addition, essential for expanding or factoring expressions.
  • Product
    The result of multiplying two or more numbers or expressions together, such as the constants in binomials.
  • Sum
    The result of adding two or more numbers, often used to match the middle coefficient in trinomials.
  • Like Terms
    Terms in an expression that have the same variable raised to the same power, which can be combined.
  • x² Term
    The squared variable part of a trinomial, always present with a coefficient of one in this factoring method.
  • T Chart
    A visual tool for organizing factor pairs to systematically find numbers that satisfy both product and sum conditions.
  • Factored Form
    An expression written as a product of simpler expressions, such as two binomials instead of a trinomial.
  • Middle Term
    The linear term in a trinomial, whose coefficient is the sum of the constants from the binomial factors.
  • Original Trinomial
    The starting three-term expression before factoring, typically written as x² plus bx plus c.