Lesson 9-2 Factoring Using the Distributive Property.

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Presentation transcript:

Lesson 9-2 Factoring Using the Distributive Property

Definitions Factoring - Factoring a polynomial means to find its completely factored form.

Use Distributive Property - 12a 2  16a First find the GCF of 12a 2 and 16a 12a 2 = 2  2  3  a  a 16a = 2  2  2  2  a GCF = 2  2  a = 4a Write the term as the product of the GCF and its remaining factors. Then use Distributive Property to factor out the GCF. 12a 2  16a = 4a (3  a)  4a (2  2) = 4a(3a)  4a(4) = 4a(3a + 4)

Use the Distributive Property to factor each polynomial A. 15x + 25x 2 B. 12xy + 24xy x 2 y 4

Factor by Grouping - Factor 4ab + 8b + 3a + 6 4ab + 8b + 3a + 6 (4ab + 8b) + (3a + 6)Find the GCF for both 4b (a + 2)  3 (a + 2)Factor the GCF from both groupings. (a + 2) (4b + 3) Use FOIL method to check..

Factor 2xy + 7x - 2y -7

Using the Additive Inverse Property - Factor 35x -5xy + 3y x -5xy + 3y - 21 = (35x -5xy) + (3y - 21) = 5x(7 - y) + 3(y - 7) = 5x(-1)(y - 7) + 3(y - 7) = -5x(y - 7) + 3(y - 7) = (y - 7)(-5x + 3)

Factor 15a - 3ab + 4b -20

Definitions Zero Product Property - If the product of two factors is 0, then at least one of the factors must be 0. Solve an Equation in Factored Form - Solve (d - 5)(3d + 4) = 0 (d - 5)(3d + 4) = 0 = d - 5 = 0 or 3d + 4 = 0 = d = 5 or 3d = -4 = d = -4/3

Solve (x - 2)(4x -1) = 0

Solve an Equation By Factoring - Solve x 2 = 7x x 2 - 7x = 0 = x (x-7) = 0 = x = 0 or x - 7 = 0 = x = 7 The solution set is {0,7}

Solve 4y = 12y 2