Number theory | Factorization

Aurifeuillean factorization

In number theory, an aurifeuillean factorization, named after Léon-François-Antoine Aurifeuille, is a special type of algebraic factorization that comes from non-trivial factorizations of cyclotomic polynomials over the integers. Although cyclotomic polynomials themselves are irreducible over the integers, when restricted to particular integer values they may have an algebraic factorization, as in the examples below. (Wikipedia).

Video thumbnail

Ex 2: Determine Factors of a Number

This is the second of three videos that provides examples of how to determine the factors of a number using a numbers prime factors. Search Video Library at http://www.mathispower4u.wordpress.com

From playlist Factors and Prime Factorization

Video thumbnail

Factoring a basic trinomial using the x method, x^2 + 8x - 9

👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic with th

From playlist Factor Quadratic Expressions

Video thumbnail

Factoring a trinomial using grouping to solve a quadratic equation

we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation. There are other methods

From playlist Solve Quadratic Equations by Factoring | ax^2+bx+c

Video thumbnail

Solving a quadratic by factoring using box method a is larger than one

we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation. There are other methods

From playlist Solve Quadratic Equations by Factoring | ax^2+bx+c

Video thumbnail

Factoring a trinomial when a is equal to two

we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation. There are other methods

From playlist Solve Quadratic Equations by Factoring | ax^2+bx+c

Video thumbnail

Ex: Factor a Polynomial Using the Grouping Technique

This video explains how to factor a polynomial using the grouping technique. Complete Video Listing: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com

From playlist Determining the Greatest Common Factor and Factoring by Grouping

Video thumbnail

How to use factoring to solve a trigonometric equation

👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq

From playlist Solve Trigonometric Equations by Factoring

Video thumbnail

How to factor a trinomial

👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic with th

From playlist Factor Quadratic Expressions

Video thumbnail

Factoring a quadratic with a not equal to one by two different methods

we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation. There are other methods

From playlist Solve Quadratic Equations by Factoring | ax^2+bx+c

Video thumbnail

Factoring Polynomials Completely - All Types (100 Problems & Free Worksheet)

Learn how to factor polynomials completely in this video math tutorial by Mario's Math Tutoring. We will be going through 100 factoring problems including greatest common factor, difference of 2 squares, sum and difference of 2 cubes, perfect square trinomials, trinomials with leading coe

From playlist Factoring - All Different Types

Video thumbnail

Factoring Trinomials with Common Factors (Form a(x+b)(x+c))

This video explains how to factor a trinomial with a common factor. After factoring out the GCF, the trinomial has a leading coefficient of 1.

From playlist Factoring Trinomials with a Leading Coefficient Not 1

Video thumbnail

Compare 3 Methods for Factoring ax^2+bx+c (a not 1, no GCF)

This video compares the methods of trial and error, grouping, and bottoms up to factor a trinomial with a not 1 and no GCF. http://mathispower4u.com

From playlist Factoring Trinomials with a Leading Coefficient Not 1

Video thumbnail

Factoring Polynomials – Lesson #1 GCF (Greatest Common Factor)

TabletClass Math: https://tcmathacademy.com/ How to factor the GCF (greatest common factor) from a polynomial. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Alg

From playlist GED Prep Videos

Video thumbnail

Finding ALL Solutions of Polynomials (Precalculus - College Algebra 37)

Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com How to completely factor a polynomial over the complex number system and find all of the solutions, including complex.

From playlist Precalculus - College Algebra/Trigonometry

Video thumbnail

Keith Conrad - Prime Factorization From Euclid to Noether

This talk was part of Number Theory Day 2023, at UConn. More information about the event can be found here: https://alozano.clas.uconn.edu/number-theory-day/

From playlist Number Theory Day

Video thumbnail

Factor by Grouping with GCF

This video provides two examples of how to factor by grouping when the original expression has a common factor. http://mathispower4u.com

From playlist Determining the Greatest Common Factor and Factoring by Grouping

Video thumbnail

The Greatest Common Factor

This video explains how to determine the GCF of integers and expressions. http://mathispower4u.wordpress.com/

From playlist Integers

Video thumbnail

Blank Editor - Project Euler Problem 3 Largest Prime Factor

Blank Editor is a show for new programmers who have trouble applying the programming concepts they've learned into real programs. This episode solves problem 3 from the Project Euler site: https://projecteuler.net/problem=3 Github repo with source code: https://github.com/asweigart/blank

From playlist Blank Editor

Video thumbnail

Factor Out The GCF (Greatest Common Factor) – Algebra – Clear and Understandable

TabletClass Math: https://tcmathacademy.com/ This video explains how to factor out the gcf (greatest common factor) a key factoring skill in algebra.

From playlist Pre-Algebra

Video thumbnail

Solving a quadratic equation using the long factoring technique

we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation. There are other methods

From playlist Solve Quadratic Equations by Factoring | ax^2+bx+c

Related pages

Perfect power | Square-free integer | Fibonacci number | Cyclotomic polynomial | Irreducible polynomial | Congruence relation | Lucas number | Édouard Lucas | Factorization | Integer | Mersenne prime | Sophie Germain | Number theory | Algebraic expression