Factor out the greatest common factor (GCF)

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Learn it Factoring is expanding in reverse. Find the greatest common factor of every term: the biggest number that divides all the coefficients, and the lowest power of each variable that appears in every term. Write it outside the brackets and divide each term by it. Check by expanding.

Example: Factor 12x³ − 18x².

GCF of 12 and 18 is 6; the lowest power of x is x².
12x³ ÷ 6x² = 2x and −18x² ÷ 6x² = −3.
So 12x³ − 18x² = 6x²(2x − 3).

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