Factoring Polynomials definitions Flashcards
Factoring Polynomials definitions
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Factoring Process of expressing a polynomial as a product of simpler polynomials whose multiplication returns the original expression. Polynomial Algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and non-negative integer exponents. Greatest Common Factor Largest expression, including numbers and variables, that evenly divides each term in a polynomial. Factor Tree Diagrammatic method for breaking down numbers or terms into their prime or irreducible factors. Grouping Factoring technique for polynomials, especially with four terms, by splitting into pairs and factoring each group separately. Standard Form Arrangement of a polynomial with terms ordered by descending powers of the variable. Difference of Squares Special product pattern where an expression is written as the subtraction of two perfect squares, factored into conjugate binomials. Sum of Cubes Special product formula for expressing the sum of two perfect cubes as a product of a binomial and a trinomial. Difference of Cubes Special product formula for expressing the difference of two perfect cubes as a product of a binomial and a trinomial. Perfect Square Trinomial Three-term polynomial fitting the pattern a² ± 2ab + b², factored as the square of a binomial. AC Method Systematic approach for factoring trinomials by finding two numbers that multiply to the product of the leading coefficient and constant, and add to the middle coefficient. Binomial Polynomial consisting of exactly two terms, typically separated by addition or subtraction. Trinomial Polynomial consisting of exactly three terms, often encountered in quadratic expressions. Distributive Property Algebraic rule allowing multiplication across terms inside parentheses, foundational for both expanding and factoring expressions. Prime Factor Factor of a number or term that cannot be broken down further, except by one and itself.
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