MathEquivalent ExpressionsHigh frequency
SAT Math: Factor out the greatest common factor
34+ practice questions in Praczo
What you need to know
The concept, explained
- 1
The GCF is the largest expression that divides every term. Look for both numerical factors and shared variables with the smallest exponent.
- 2
For 6x³ + 9x², the GCF is 3x² — divide each term: 3x²(2x + 3).
- 3
Always factor out the GCF before trying any other factoring method; missing it often leaves you with unnecessarily ugly numbers.
- 4
Check your result by distributing: if it doesn't rebuild the original, re-factor.
Common mistakes
- ✗ Taking a GCF that's too small (e.g., pulling out x² when 3x² is also common).
- ✗ Forgetting to include every term inside the parenthesis when you factor (especially a trailing "1" when you factor out the whole term).
Try a sample question
SAT-style practice
Which expression is equivalent to 12x³y − 18x²y²?
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