Glencoe Algebra 1 Chapter 8 Vocabulary

Algebra Vocabulary

Binomial: A mathematical expression consisting of two monomials combined by addition or subtraction.
Polynomial: An algebraic expression made up of one or more monomials, which may include constants, variables, and positive integer exponents.
Degree of a Monomial: Calculated by summing the exponents of all variables within the monomial.
Prime Polynomial: A polynomial that cannot be factored into the product of two polynomials with integer coefficients, indicating it has no non-trivial factors.
Degree of a Polynomial: Identified as the highest degree among all its terms, determining the polynomial's overall complexity.
Quadratic Equation: Defined as an equation that can be expressed in the standard form ax² + bx + c = 0, where 'a' is non-zero.
Difference of Two Squares: A factorization method for expressions of the form a² - b², which factors into (a + b)(a - b).
Quadratic Expression: An algebraic expression represented in the form ax² + bx + c, where the variable's degree is 2.
Factoring: The process of rewriting a polynomial as a product of simpler monomials and/or polynomials.
Square Root Property: A technique used to solve quadratic equations of the form x² = n by taking the square root of both sides.
Factoring by Grouping: A method of factoring that utilizes the distributive property on polynomials with four or more terms to simplify them into products.
Standard Form of a Polynomial: A structured format where polynomial terms are arranged from the highest degree to the lowest degree.
FOIL Method: A technique specifically for multiplying two binomials by taking the sum of the products of the First, Outer, Inner, and Last terms.
Trinomial: An algebraic expression containing three monomials combined by addition or subtraction.
Leading Coefficient: The coefficient associated with the term that has the greatest degree within a polynomial, influencing the polynomial's end behavior.
Zero Product Property: A principle stating that if the product of multiple factors equals zero, then at least one factor must be zero.
Perfect Square Trinomial: A trinomial that can be expressed as the square of a binomial, characterized by forms such as (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².