College Algebra / Unit 2 Alg 083 worked example, 60 to 90 seconds
Factoring Out the GCF
The idea
Factoring out the GCF means identifying the greatest common factor, writing it outside parentheses, and filling the parentheses with each term divided by it.
In practice
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.
Where people slip
Every term must surrender the factor; one holdout means the candidate was too big.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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