Transcript 10.5 Factoring x2 + bx + c

8.5 Factoring Trinomials of the
type x2 + bx + c
Objective: SWBAT solve a
quadratic equation by
factoring.
Mini Quiz 12
1.
1.
2.
CAHSEE Review
Overview
Factoring x2 + bx + c…(no GCF)
 Using the “X” Factor
 4 Lines Factoring
 Reverse FOIL
Factoring with the “X”
Factor x2 – x – 6
a =1
b = -1
c = -6
+2
Steps:
1. Draw your “X”
-1
b
2. Fill in the a, b, c
+
(ax2 + bx + c)
x
3. Write the Factor
-3
-6
a·c
(x + 2)(x – 3)
Factoring with the “X”
Factor
1. x2 – 5x + 6
2. x2 – 6x + 9
3. x2 – 16
4. x2 – 6x – 16
(x – 2) (x – 3)
(x – 3)2
(x + 4) (x – 4)
(x – 8) (x + 2)
+
x
4 Line Factoring
Factor x2 – x – 6
Steps:
1. Write the trinomial on top
2. Write the “b” term on the
bottom
3. Think: “what two things
multiply to the “a” term
4. Think: “What two things
multiply to the “c” term
5. Cross multiply to check
x2 – x – 6
x
–3
x
+2
-3x
2x
– x
(x – 3) (x + 2)
4 Line Factoring
Factor
5. x2 – 10x + 25
6. x2 + 6x – 27
7. x2 + 4x + 4
8. x2 – 4
(x – 5) (x – 5)
(x + 9) (x – 3)
(x + 2)2
(x + 2) (x – 2)
Factoring by Reverse FOIL
Factor x2 – x – 6
Steps:
1. Set up your ( )( )
2. Guess factors for F
3. Guess factors for L
4. Check O and I
( x – 3)( x+ 2)
-3x
+2x
= -x 
(x – 3)(x + 2)
Factoring by Reverse FOIL
Factor
9. x2 + 11x + 10
10. x2 – 17x + 60
11. x2 – 49
12. x2 – 12x + 36
(x + 10)(x + 1)
(x – 12)(x – 5)
(x – 7)(x + 7)
(x – 6)2
Wrap Up (
)(
Factoring
- “X” Factor
- Using 4 lines method
- Reverse FOIL
HW: P. 397 #1-37 EOO;
P. 407 #1-6 all; 13-18 all
Write DLUQ for notes
)
+
x