Algebra 1: Polynomials and Factoring

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.