Factoring Polynomials Flashcards

Questions and Answers

What is a binomial?

An algebraic expression consisting of three terms

An algebraic expression consisting of two terms (correct)

An algebraic expression consisting of one term

A finite sum of terms

What is a common factor?

Factor that repeatedly occurs in each term

What is a factor?

An exact divisor of a number

What are factors?

Terms to be multiplied to give the polynomial Signup and view all the answers

What does factoring mean?

Process of finding factors of a polynomial Signup and view all the answers

What is the greatest common factor (GCF)?

The greatest integer that is a factor of all the given integers Signup and view all the answers

What is the greatest common monomial factor (GCMF)?

The greatest factor contained in every term of an algebraic expression Signup and view all the answers

What is a monomial?

An algebraic expression consisting of one term Signup and view all the answers

What is a polynomial?

A finite sum of terms each of which is a real number or the product of a numerical factor and one or more variable factors raised to a whole number power Signup and view all the answers

What is a prime number?

Is a number greater than one which has only two positive factors: 1 and itself Signup and view all the answers

What is a prime polynomial?

An irreducible polynomial with integral coefficients whose greatest monomial factor is 1 Signup and view all the answers

What is a trinomial?

An algebraic expression consisting of three terms Signup and view all the answers

Study Notes

Key Concepts in Factoring Polynomials

Binomial: Represents an algebraic expression with two distinct terms, essential in polynomial equations.
Common Factor: Identifies a factor that appears in all terms of an expression, crucial for simplifying polynomials.
Factor: Refers to a number that divides another number without leaving a remainder, foundational in arithmetic and algebra.
Factors of a Polynomial: Terms multiplied together to produce a polynomial; understanding this is key for polynomial manipulation.
Factoring: The process of decomposing a polynomial into products of its factors to simplify or solve equations.
Greatest Common Factor (GCF): The largest integer that divides all the given integers, used to streamline polynomial expressions.
Greatest Common Monomial Factor (GCMF): The largest monomial shared by all terms of an algebraic expression, instrumental in polynomial factoring.
Monomial: A fundamental algebraic expression consisting of a single term, often used in polynomial construction.
Polynomial: Defined as a finite sum of terms, each being a product of a numerical factor and one or more variables raised to whole number powers.
Prime Number: A number greater than one with only two distinct positive divisors: one and itself, significant in number theory.
Prime Polynomial: A polynomial that cannot be factored into simpler polynomials with integer coefficients, emphasizing its irreducibility.
Trinomial: An algebraic expression made up of three terms, commonly encountered in polynomial equations.

Description

This quiz focuses on key terms related to factoring polynomials, including definitions for binomials, common factors, and the factoring process. Enhance your understanding of algebraic expressions and their components as you review these essential concepts.