8.6 Factoring Trinomials of the type ax2 + bx + c

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Presentation transcript:

8.6 Factoring Trinomials of the type ax2 + bx + c Objective: SWBAT solve a quadratic equation by factoring.

Mini Quiz 8 1. Laura has 25 marbles. Paul has x marbles. Together they have a total of 50 marbles. Which equation can be used to determine the number of marbles Paul has? 2. Multiply

CAHSEE Review

Overview Factoring ax2 + bx + c Check for GCF (Greatest Common Factor) Factor by: 4 Lines Reverse FOIL X  Box X  Grouping

Factoring Trinomials of the Type ax2 + bx + c Steps: Check for GCF - Reverse Distribute Factor - ( )( )

4 Lines Method 1. Factor 12x2 – 38x + 30 2(6x2 – 19x + 15) 2 (2x – 3) - 3 -9x 3x - 5 -10x -19x

( )( ) 2x – 5 2x + 5 -10x 10x ( )( ) 2x – 5 2x + 5 Reverse FOIL b = 0 2. Factor 4x2 – 25 b = 0 ( )( ) 2x – 5 2x + 5 -10x 10x ( )( ) 2x – 5 2x + 5

x + 5 11 b 2x2 10x 2x +1 +10 +1 1x 5 a·c 10 (x + 5) (2x + 1) X  Box Method (when a ≠ 1) 3. Factor 2x2 + 11x + 5 a = b = c = 2 x + 5 11 11 b 2x2 10x 2x 5 + +1 +10 +1 1x 5 x a·c 10 (x + 5) (2x + 1)

-7 b -4 - 3 a·c 12 X  Grouping (a ≠ 1) ( ) 2x2 – 3x + – 4x + 6 ( ) x 4. Factor 22x2 – 77x + 66 a = b = c = = 11(2x2 – 7x + 6) -7 b 2 -7 + -4 - 3 6 x a·c 12 ( ) 2x2 – 3x + – 4x + 6 ( ) x (2x – 3) + -2 (2x – 3) (2x – 3) (x – 2) (2x – 3) (x – 2) 11

Practice Problems (use the method of your choice) Factor 5. 6x2 – 19x + 15 6. 2x2 – 4x – 6 7. 2x2 – 8 8. x2 – 2x – 3 (2x – 3)(3x – 5) 2(x – 3)(x + 1) 2(x – 2)(x + 2) (x – 3)(x + 1)

Wrap Up ( ) ( ) Factoring ax2 + bx + c Check for GCF (Greatest Common Factor) Factor by: Using 4 lines method Reverse FOIL X  Box X  Grouping HW: P. 401 #1-25 EOO, P. 409 #31-36 all DLUQ: What’s the first thing to look for before factoring into ( )( )? ( ) ( )