1. 8.6 Factoring Trinomials of the type ax2 + bx + c
Objective: SWBAT solve a quadratic equation by factoring.

2. 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

3. CAHSEE Review

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

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

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

7. ( )( ) 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

8. 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)

9. -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

10. 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)

11. 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 #1-25 EOO,
P #31-36 all
DLUQ: What’s the first thing to look for before factoring into ( )( )?
( ) ( )