8 6 Factoring Trinomials of the type ax

8. 6 Factoring Trinomials of the type ax 2 + 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 ax 2 + bx + c n Check for GCF (Greatest Common Factor) n Factor by: q q 4 Lines Reverse FOIL X Box X Grouping

Factoring Trinomials of the Type ax 2 + bx + c Steps: 1. Check for GCF - Reverse Distribute 2. Factor - ( )( )

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

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

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

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

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

Wrap Up + x Factoring ax 2 + bx + c n Check for GCF (Greatest Common Factor) n Factor by: Using 4 lines method ( ) q Reverse FOIL q X Box q 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 ( )( )? q