College Algebra / Alg 083 · Procedure · 60–90 seconds
Factoring Out the GCF
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Factoring out the GCF means identifying the greatest common factor, writing it outside parentheses, and filling the parentheses with each term divided by it.
Factor 12x³ + 18x². The GCF of the terms is 6x². Divide each term: 12x³/6x² = 2x, and 18x²/6x² = 3. Write the product: 6x²(2x + 3). Multiply back to check: 6x² · 2x = 12x³ and 6x² · 3 = 18x² — the original returns, so the factoring stands. Run this move first on every factoring problem: a leftover common factor hides every pattern the later methods hunt for, and pulling it out early keeps the remaining numbers small. Two terms or ten, the procedure is identical: find, divide, rewrite, multiply back.
Every term must surrender the factor; one holdout means the candidate was too big.
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