# alg14.ppt - Greatest Common Factor (GCF) The Distributive...

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1Greatest Common Factor (GCF)The Distributive Property says that:3y(4y + 3x + 6) = 12y2+ 9xy + 18yIn 12y2+ 9xy + 18y do you see 3y as thegreatest common factor?We can reverse the process and say that:12y2+ 9xy + 18y = 3y(4y + 3x + 6)This is called factoring out the GCF
2The Undistributive Property?8x3+ 2x2+ 4x has a common factor, 2xSo it can be rewritten as 2x(4x2+ x + 2)We undistributed or gathered the 2xWhat is the gcf of 2x3y2+ 6x2y2+ 8x2y4?Write it in factored formTry p36, #4, 6, 8, 10, and 2
3Factoring 2ndDegree TrinomialsUsing the FOIL method(3x + 4)(x + 2) = 3x2+ 6x + 4x + 8 or3x2+ 10x + 8Factoring is the reverse processHow do we get from3x2+ 10x + 8 to (3x + 4)(x + 2) ?The product of 3x and x make 3x2And 2 x 4 = 8 but what about the 10x?The 10x is the sum of thecross products(outers and inners), 6x and 4x
4Factoring as Trial and Error2x2+ 11x + 12 could factor as:(2x + 6)(x + 2)(2x - 6)(x - 2)(2x + 2)(x + 6)(2x - 2)(x - 6)(2x + 4)(x + 3)(2x - 4)(x - 3)(2x + 3)(x + 4)(2x - 3)(x - 4)+10x-10x+14xCross Products-14x+10x-10x+11x-11x

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Term
Fall
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Tags
Perfect square, Greatest common divisor, Distributivity
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