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Factoring by Greatest Common Factor & Grouping definitions

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  • Polynomial
    An expression made up of terms with variables and coefficients, often combined using addition or subtraction.
  • Term
    A single part of an expression, usually consisting of a coefficient and variable(s) with exponents.
  • Coefficient
    A numerical factor that multiplies a variable or variables in a term.
  • Variable
    A symbol, often a letter, representing an unknown value in an expression or equation.
  • Exponent
    A number indicating how many times a variable is multiplied by itself within a term.
  • Prime Factorization
    A breakdown of a number or term into a product of prime numbers and variables.
  • Greatest Common Factor
    The largest factor shared by all terms in an expression, including both numbers and variables.
  • Factored Form
    An expression rewritten as a product of its factors, making it easier to simplify or solve.
  • Grouping
    A method for factoring polynomials by pairing terms and extracting common factors from each pair.
  • Binomial
    An expression consisting of two terms joined by addition or subtraction.
  • FOIL
    A technique for multiplying two binomials, involving First, Outside, Inside, and Last terms.
  • Distributive Property
    A rule allowing multiplication across terms inside parentheses, used to expand or check factored expressions.
  • Product
    The result of multiplying two or more numbers, variables, or terms together.
  • Factor
    A number or variable that divides another term evenly, often used to simplify expressions.
  • Check
    A process of verifying the accuracy of factoring by expanding the expression and comparing to the original.