Factoring Fundamentals
Factoring Completely
To factor completely means to continue until none of the factors can be factored any further using the method you are learning.
When is an expression fully factored?
A factorization is incomplete when the terms inside the parentheses still share a factor. For example, 2(3x + 6) is not complete because 3x and 6 still share 3.
How to check your factorization
- Find the greatest common factor, not just any common factor.
- Divide every term correctly.
- Check the expression inside the parentheses for another shared factor.
- Expand to confirm that you recover the original expression.
Worked example
Factor 8x + 12 completely
- The GCF of 8 and 12 is 4.
- 8x ÷ 4 = 2x.
- 12 ÷ 4 = 3.
8x + 12 = 4(2x + 3), and 2x + 3 has no common factor greater than 1.
Common mistakes
- Stopping after taking out 2 when a larger factor can come out.
- Assuming an answer is complete without checking inside the parentheses.
Practice more
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