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Factoring by Greatest Common Factor & Grouping definitions

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  • Polynomial
    An expression made up of terms, each consisting of a coefficient, variable, and exponent, combined using addition or subtraction.
  • Greatest Common Factor
    The largest factor that evenly divides every term in a polynomial, including both numbers and variables.
  • Prime Factorization
    A breakdown of a number or term into a product of prime numbers and variables, often used to identify common factors.
  • Coefficient
    A numerical value multiplied by a variable in a term, indicating the term's magnitude.
  • Exponent
    A value showing how many times a variable is multiplied by itself within a term.
  • Term
    A single part of a polynomial, composed of a coefficient, variable, and possibly an exponent.
  • Binomial
    An expression consisting of exactly two terms joined by addition or subtraction.
  • Factored Form
    A representation of a polynomial as a product of simpler expressions or factors.
  • Grouping
    A technique for factoring polynomials with four terms by pairing and extracting common factors from each pair.
  • Redistribution
    A process of multiplying factored expressions to verify the original polynomial is obtained.
  • FOIL Method
    A technique for multiplying two binomials by combining First, Outer, Inner, and Last terms.
  • Standard Form
    A way of writing a polynomial with terms ordered by descending exponents.
  • Variable
    A symbol representing an unknown value, often used with exponents and coefficients in polynomials.
  • Factor
    A number or variable that divides another term or expression without leaving a remainder.
  • Product
    The result of multiplying two or more numbers, terms, or expressions together.