F i v e o r m s o f a c t o r i n g.

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Presentation transcript:

F i v e o r m s o f a c t o r i n g

1. Greatest Common Factor (GCF) Ex 1 10x2y3z - 8x4y2 (5yz - 4x2) 2x2y2 Ex 2 15a2b5 + 5ab2 - 25a3b4 (3ab3 + 1 - 5a2b2) 5ab2

2. Factoring Trinomials Ex 1 x2 - 15x + 36 ( )( ) x - 12 - 3 Ex 2 6x2 + 11x - 10 ( )( ) 2x 3x + 5 - 2 Ex 3 10x3 - 26x2 + 12x 2x(5x2 - 13x + 6) 2x ( )( ) 5x x - 3 - 2

3. The Difference of Two Squares Ex 1 x2 - 36 (x + 6)(x - 6) ( )( ) 2a 2a + 9b - 9b Ex 2 4a2 - 81b2 a4 - b6 ( )( ) a2 a2 + b3 - b3 Ex 3 (n4 + 1) (n4 - 1) Ex 4 n8 - 1 (n4 + 1) (n2 + 1)(n2 - 1) (n4 + 1)(n2 + 1) (n + 1)(n - 1)

4. Factoring By Grouping Ex 1 b3 - 3b2 + 4b - 12 group factor out (b3 - 3b2) + (4b - 12) b2(b - 3) + 4(b - 3) GCF now is (b - 3) (b - 3) (b2 + 4) Ex 2 4ax + 14ay - 10bx - 35by (4ax + 14ay) - (10bx - 35by) 2a(2x + 7y) - 5b(2x + 7y) (2x+7y)(2a-5b)

5. The Sum & Difference of Cubes Ex 1 x3 - 8 ( ) ( ) x x2 - 2 + 2x + 4 Ex 2 27a3 + b3 ( ) ( ) 3a + b 9a2 - 3ab + b2 Ex 3 2 + 128y6 2(1 + 64y6) 2( ) ( ) 1 1 + 4y2 - 4y2 + 16y4

Factoring 1. Greatest Common Factor (GCF) 2x2y3-6xy2 = 2xy2 (xy - 3) 2. Factoring Trinomials 6x2 + 11x - 10 = ( )( ) 2x 3x + 5 - 2 3. The Difference of Two Squares 4a2 - 81b2 = ( )( ) 2a 2a + 9b - 9b 4. Factoring By Grouping b3 - 3b2 + 4b - 12 = (b - 3) (b2 + 4) 5. The Sum & Difference of Cubes x3 - 8 = ( ) ( ) x x2 2 4 2x - +