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Factoring Polynomials definitions Flashcards

Factoring Polynomials definitions
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  • Polynomial
    An algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
  • Factoring
    The process of breaking down a complex algebraic expression into simpler expressions whose product is the original expression.
  • Greatest Common Factor
    The largest expression that evenly divides each term in a polynomial, including both numerical and variable components.
  • Factor Tree
    A diagrammatic method for breaking down numbers or terms into their prime or irreducible factors.
  • Grouping
    A factoring technique where terms are separated into pairs or groups to extract common factors from each group, often used for four-term polynomials.
  • Standard Form
    An arrangement of a polynomial with terms ordered by descending powers of the variable.
  • Binomial
    An algebraic expression composed of exactly two terms, typically joined by addition or subtraction.
  • Trinomial
    An algebraic expression composed of exactly three terms, usually in the form ax^2 + bx + c.
  • AC Method
    A systematic approach for factoring trinomials by multiplying the leading coefficient and constant, then finding two numbers that multiply to this product and add to the middle coefficient.
  • Perfect Square Trinomial
    A trinomial that can be written as the square of a binomial, following the pattern a^2 ± 2ab + b^2.
  • Difference of Squares
    An expression in the form a^2 - b^2, which factors into (a + b)(a - b).
  • Difference of Cubes
    An expression in the form a^3 - b^3, which factors into (a - b)(a^2 + ab + b^2).
  • FOIL Method
    A technique for multiplying two binomials by multiplying First, Outer, Inner, and Last terms and summing the results.
  • Prime Factor
    A factor that cannot be broken down further, either a prime number or an irreducible variable factor.
  • Common Factor
    A number or variable that appears in each term of a polynomial, allowing for extraction during factoring.