Factoring by Grouping Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Factoring by Grouping.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A factoring technique for polynomials with four or more terms: group terms into pairs, factor the GCF from each pair, then factor out the common binomial factor.
Imagine four terms that seem unrelated. By cleverly grouping them into two pairs and factoring each pair separately, a common binomial factor often emerges—like finding a hidden pattern by rearranging puzzle pieces.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: After factoring each group, the remaining binomial factors must match—if they do not, try rearranging the terms or a different grouping.
Common stuck point: If the binomial factors from each group do not match, the terms may need to be rearranged, or the polynomial may not factor by grouping.
Sense of Study hint: Split the four terms into two pairs, factor each pair, and check whether the leftover binomials match.
Worked Examples
Example 1
mediumSolution
- 1 Step 1: Group into pairs: (x^3 + 3x^2) + (2x + 6).
- 2 Step 2: Factor each group: x^2(x + 3) + 2(x + 3).
- 3 Step 3: Factor out the common binomial: (x^2 + 2)(x + 3).
- 4 Check: (x^2+2)(x+3) = x^3 + 3x^2 + 2x + 6 ✓
Answer
Example 2
hardPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.