Factoring Fundamentals
Factoring Out the GCF
Factoring out the GCF rewrites a sum as multiplication. You place the greatest factor shared by every term outside parentheses, then divide each term by it.
Why factor out the GCF?
Factoring reverses distribution. Since 3(2x + 3) expands to 6x + 9, the expression 6x + 9 can be factored as 3(2x + 3).
How to factor out the GCF
- Find the GCF of all coefficients and variables.
- Write the GCF outside parentheses.
- Divide every original term by the GCF.
- Place the quotients inside the parentheses.
- Expand once to check your answer.
Worked example
Factor 10x + 15
- GCF(10, 15) = 5
- 10x ÷ 5 = 2x
- 15 ÷ 5 = 3
10x + 15 = 5(2x + 3).
Common mistakes
- Dividing only the first term.
- Taking out a common factor that is not the greatest one.
- Changing a sign while dividing.
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