Factoring
Factor polynomials, trinomials, and special products
lessons (12)
Introduction to Factoring
Learn what factoring is and how to break down expressions into their component factors.
Factoring Out the GCF
Learn to identify and factor out the greatest common factor from polynomial expressions.
Factoring by Grouping
Learn how to factor polynomials with four terms by grouping pairs that share common factors.
Factoring Trinomials (a=1)
Learn to factor quadratic trinomials where the leading coefficient is 1.
Factoring Trinomials (General)
Learn to factor trinomials when the leading coefficient is not 1 using the AC method.
Difference of Squares
Learn to recognize and factor expressions in the form a squared minus b squared.
Perfect Square Trinomials
Learn to recognize and factor trinomials that are perfect squares of binomials.
Sum and Difference of Cubes
Learn to factor expressions in the form a³ + b³ and a³ - b³ using special formulas.
Factoring Completely
Learn to combine all factoring techniques to factor any polynomial expression completely.
Zero Product Property
Learn how the zero product property helps you solve quadratic equations by setting each factor equal to zero.
Solving Equations by Factoring
Learn how to solve quadratic equations by factoring them into products of binomials and applying the zero product property.
Factoring Word Problems
Apply factoring techniques to solve real-world problems involving area, projectile motion, and number relationships.
Factoring is the process of breaking down algebraic expressions into simpler components that multiply together to give the original expression. It's the reverse of multiplication and is crucial for solving equations, simplifying fractions, and understanding polynomial behavior. Factoring skills are essential for algebra, calculus, and beyond.
In this topic, you will learn multiple factoring techniques: finding greatest common factors, factoring trinomials, recognizing special patterns like difference of squares, and handling more complex expressions. Each method has its place, and knowing when to apply each one is a key problem-solving skill.
Our lessons build factoring intuition through visual models and pattern recognition. You will practice with increasingly complex expressions, develop strategies for choosing the right technique, and learn to verify your factoring by multiplication. These skills form the foundation for solving quadratic equations and working with rational expressions.
What Students Will Learn
- Factor out the greatest common factor (GCF)
- Factor trinomials of the form x² + bx + c
- Factor trinomials of the form ax² + bx + c
- Recognize and factor difference of squares
- Recognize and factor perfect square trinomials
- Factor by grouping for four-term expressions
- Combine multiple factoring techniques
Frequently Asked Questions
Why is factoring important?
Factoring is essential for solving quadratic equations, simplifying algebraic fractions, and finding zeros of polynomials. It reveals the structure of expressions and is used throughout advanced mathematics.
How do I know which factoring method to use?
Start by looking for a GCF. Then check the number of terms: two terms might be difference of squares, three terms could be a trinomial pattern, four terms often factor by grouping. Practice helps you recognize patterns quickly.
How can I check my factoring?
Multiply your factors back together—you should get the original expression. This verification step catches errors and builds confidence in your factoring skills.