Factoring by the Greatest Common Factor

Mathematics — Second Preparatory

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Factor 6x + 9	Factor
Solution	The GCF of the coefficients 6 and 9 is 3 and x does not appear in the second term. So 6x + 9 = 3(2x + 3)	coefficientsdoesappearsecond
Example 2	Factor 12a²b − 18ab²	Factor12a²b18ab²
Solution	The GCF of 12 and 18 is 6. The smallest power of a is 1 and the smallest power of b is 1. So the GCF is 6ab and the factored form is 6ab(2a − 3b). Check: 6ab × 2a = 12a²b and 6ab × 3b = 18ab²	smallestpowerfactoredform
Example 3	Factor x(x + 2) − 3(x + 2)	Factor
Solution	The common factor is the bracket (x + 2). So the factored form is (x + 2)(x − 3)	commonfactorbracketfactored
Example 4	Factor 4x³ − 8x² + 12x	Factor
Solution	The GCF of 4 8 and 12 is 4 and the smallest power of x is 1. So we take out 4x: 4x(x² − 2x + 3). The expression inside the bracket has no common factor left so the factoring is complete	smallestpowertakeexpression

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