Factoring a Greatest Common Factor

Algebra Foundation

Algebra 1

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Algebra 1 · Unit 8 · Topic 8.1

Factoring a Greatest Common Factor

Factoring rewrites a sum as a product.

Definition and explanation

Factoring rewrites a sum as a product. First check for a greatest common factor shared by all terms; factoring is verified by multiplying the factors back out.

Worked example

Factor 12x³ − 18x². The coefficient GCF is 6 and the shared variable power is x², so the result is 6x²(2x − 3). Distribution reproduces both original terms.

Common mistake

Take out a factor common to every term, not just a selected pair.

Key takeaway

Factoring rewrites a sum as a product.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.