Factoring Out the GCF
Pull the greatest common factor out of every term.
Key idea
Pull the greatest common factor out of every term.
In depth
Factoring reverses distribution. Find the greatest common factor of all terms, put it outside brackets and divide each term. Always do this first.
Worked example
6x³ + 9x² = 3x²(2x + 3).
Formula
Real-world uses
- Simplifying formulas for area or cost by pulling out a common factor before solving
Common mistake
Pulling out a factor that is not the greatest, leaving more factoring to do.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Factoring Out the GCF?
Pull the greatest common factor out of every term. It is a topic at the intermediate level in Algebra.
What is the formula for Factoring Out the GCF?
The key formula is 6x²+9x = 3x(2x+3).
Where is Factoring Out the GCF used in real life?
Real-world examples: Simplifying formulas for area or cost by pulling out a common factor before solving.
What should I learn before Factoring Out the GCF?
Make sure you are comfortable with Special Products, the previous topic in Algebra.
What is a common mistake with Factoring Out the GCF?
Pulling out a factor that is not the greatest, leaving more factoring to do.
How can I practise Factoring Out the GCF?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Factoring Out the GCF?
Move on to Factoring Trinomials next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.