What you’ll learn
Factor linear expressions.
Key idea
Find the greatest common factor shared by the coefficients and place it outside parentheses. Divide each original term by that factor to determine what remains inside. Include variable factors shared by every term when appropriate.
For 12x + 18, the greatest common factor of 12 and 18 is 6. Dividing gives 2x and 3, so the factored expression is 6(2x + 3). Distribute to check: 12x + 18. A factorization is useful when it exposes a common structure or makes later operations easier.
Worked example
Enter the exact value or ordered values in the format requested below.
Factor -6x-8 using its positive greatest common numerical factor. Enter the factored form, not an expanded equivalent.
- The positive greatest common factor of |-6| and |-8| is 2.
- Divide both signed coefficients by 2: 2(-3x-4) expands to -6x-8.
Answer: 2(-3x-4)
Quick Check
Evaluate a worked attempt at factor linear expressions, identify the first invalid step, and provide the correction.
Step 1: GCF(|2|,|-6|)=2. Step 2: 2x-6=2(1x-6), leaving the original constant inside. Locate the first invalid step and correct the factorization.