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Math 126 Factoring Polynomials Types of Factoring 1)Factor by taking out a Greatest Common Factor (GFC)2)Factor a trinomial as two binomials. 3)Factor a binomial as a difference of two squares 4)Factor a binomial as a difference of cubes or a sum of cubes Factoring out a Greatest Common FactorTaking out a greatest common factor is essentially the same as working the distributive property backwards. Review of distributive property 153533)5(3+=⋅+=+xxxExample 1 Factor out a greatest common factor 164+xSolution: )4(4164+=+xxExample 2 Factor out a greatest common factor 355−xSolution:)7(5355−=−xxExample 3 Factor out a greatest common factor xxx168223+−Solution:)84(21682223+−=+−xxxxxx
Example 4 Factor out a greatest common factor xyyxyx482412223++ Solution:)42(124824122223++=++xyxxyxyyxyxFactoring a trinomial as two binomialsFactoring a trinomial is the same as working the FOIL process So, here is a short review of FOIL()()127124343344322++=++⋅+++⋅++xxxxxxxxxxxExample of factoring a trinomial as two binomials Factor 25102++xxIn this example you want to find two numbers that multiply to get 25 and add to get 10. By using x as the first entry in each binomial you get: ()()5525102++=++xxxxHere are some similar examples Example 5 Factor 24102+−xxAnswer: ()()46−−xx Hint: Find two numbers that multiply to get 24 and add to get -10

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