Factoring Out the GCF Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Factoring Out the GCF.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Factoring out the greatest common factor (GCF) means identifying the largest expression that divides every term, then rewriting the polynomial as that GCF times what remains.
Look at what all terms share in common—like taking the common ingredient out of a recipe. In 6x^3 + 9x^2, every term has at least 3x^2 in it, so pull it out front: 3x^2(2x + 3).
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: Always look for the GCF first—it is the first step in any factoring problem.
Common stuck point: Finding the GCF of both the coefficients AND the variable parts. The GCF of 6x^3 and 9x^2 is 3x^2, not just 3 or x^2.
Sense of Study hint: Find the GCF of the coefficients first, then find the lowest power of each variable that appears in every term.
Worked Examples
Example 1
easySolution
- 1 Step 1: Find the GCF of 6x^2 and 9x: GCF of 6 and 9 is 3; both have at least x. GCF = 3x.
- 2 Step 2: Divide each term: 6x^2 \div 3x = 2x and 9x \div 3x = 3.
- 3 Step 3: Write as product: 3x(2x + 3).
- 4 Check: 3x(2x + 3) = 6x^2 + 9x ✓
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.