Algebra 1: Polynomials and Factoring

Questions and Answers

What is a binomial?

A polynomial with one term

A polynomial with four terms

A polynomial with three terms

A polynomial with two terms (correct)

What is the degree of a monomial?

Sum of the exponents and its variables

A monomial is an expression with only two terms.

False

What is a polynomial?

A monomial or the sum of monomials Signup and view all the answers

A polynomial in one variable is written in standard form when the terms are in order from greatest _____ to least degree.

degree Signup and view all the answers

What method can be used for multiplying binomials?

Distributive property Signup and view all the answers

Define the square of a binomial.

The square of the first term plus twice the product of the two terms plus the square of the last term Signup and view all the answers

What is the product of a sum and difference?

The difference of their squares Signup and view all the answers

What is a difference of two squares?

A polynomial that can be factored as the product of the sum and difference of two terms Signup and view all the answers

What is factoring by grouping?

The process of factoring four terms by grouping them in pairs Signup and view all the answers

What is a perfect square trinomial?

A trinomial that is the result of squaring a binomial Signup and view all the answers

Study Notes

Polynomials and Factoring

Binomial: A polynomial composed of two distinct terms.
Degree of a Monomial: Calculated by summing the exponents of all variables within the term.
Monomial: An algebraic expression that consists of a single term without any addition or subtraction.
Polynomial: Can either be a single monomial or comprised of multiple monomials combined through addition or subtraction.
Standard Form of a Polynomial: A polynomial is considered to be in standard form when its terms are arranged in descending order based on their degrees.
Multiplying Binomials: The distributive property is the method used to multiply two binomials, ensuring each term in the first binomial is multiplied by each term in the second.
Square of a Binomial: The expansion of a binomial squared results in the first term squared, plus twice the product of the two terms, plus the last term squared.
Product of a Sum and Difference: When multiplying a sum and a difference of the same two terms, the result is equivalent to the difference of their squares.
Difference of Two Squares: This polynomial form can be factored into the product of the sum and the difference of the two terms involved.
Factoring by Grouping: This technique is utilized to factor expressions with four terms by pairing them, extracting the greatest common factor (GCF) from each pair, and identifying a shared binomial factor.
Perfect Square Trinomial: A specific type of trinomial formed from the squaring of a binomial, showcasing a particular structure in its coefficients.

Description

Test your knowledge of polynomials and their properties with this flashcard quiz. Learn key terms such as binomials, monomials, and polynomial standard forms. Perfect for Algebra 1 students aiming to master these essential concepts.