Factoring polynomials can be challenging, especially when an expression contains four terms instead of the usual two or three. But what if you could break a complicated polynomial into smaller groups and use something you already know—the greatest common factor (GCF)—to factor the entire expression?
In this video, you’ll learn how to factor polynomials using factoring by grouping, a method that allows you to organize four-term polynomials into pairs, factor out common factors, and identify a shared binomial. Rather than guessing at possible factors, factoring by grouping provides a structured, step-by-step approach to rewriting polynomial expressions as products of simpler factors.
We’ll walk through the process step by step, showing how to group terms, factor out the GCF from each group, identify the common binomial, and complete the factoring process. You’ll also see why the method works by connecting it to the distributive property.
In this lesson you’ll learn:
• What factoring by grouping is and when to use it
• How to recognize polynomials that can be factored by grouping
• How to organize four-term polynomials into two groups
• How to identify and factor out the greatest common factor (GCF) from each group
• Why both groups must contain a matching binomial factor
• How to recognize when a negative GCF is needed
• How to factor out the common binomial to write the final factored expression
• How factoring by grouping connects to the distributive property
• How to check your answer by multiplying the factors
• Common mistakes students make when factoring by grouping
By the end of this lesson, you’ll understand how factoring by grouping works and how to use it to factor four-term polynomials efficiently and accurately. You’ll also recognize why identifying common factors and organizing expressions into smaller pieces can make complicated algebra problems easier to solve.
Whether you’re taking Algebra 1, Algebra 2, Honors Algebra 2, Precalculus, or preparing for the ACT or SAT, understanding factoring by grouping is an important skill that strengthens your ability to work with polynomial expressions and equations.
