1. Warmup
Factor. 1. GCF 2. GCF 3. Grouping/GCF 4. Grouping

2. 4.4 Factoring Trinomials Day 3 a=1 and a>1
Objective: To factor quadratic trinomials.

3. Remember…
(x+2)(x+5) We used double distribution to multiply this. Today, we are going to work BACKWARDS!  New method…. The X!!

4. Example 1 1st•3rd 2nd 45 9 5 14 (x + 9)(x + 5) x2 + 14x + 45
Pick 2 #s that multiply to get the top and add to get the bottom.
Those go on the sides of the X.
(x + 9)(x + 5)

5. When a=1 you don’t have to use the box
No box is necessary
When a>1 you have to use the x and the box

6. When a>1 you must use the x and the box.
This song will “teach you how to factor”

7. First and Last Coefficients
Factor the x-box way
y = ax2 + bx + c
Base 1
Base 2
Product
ac=mn
First and Last Coefficients
1st Term
Factor n
GCF n m
Middle
Last term
Factor m
b=m+n
Sum
Height

8. Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)= -30 x -5
-15 2
-13 2x
-10 +2
3x2 -13x -10 = (x-5)(3x+2)

9. Examples Factor using the x-box method. 1. x2 + 4x – 12 x +6 x2 6x x
a) b) x +6
-12 4
x x
-2x x 6 -2 -2
Solution: x2 + 4x – 12 = (x + 6)(x - 2)

10. Examples continued x -4 x x2 -4x -5x 20
a) b) x -4 20 -9 x
x2 -4x
-5x 20 -5
Solution: x2 - 9x + 20 = (x - 4)(x - 5)

11. Think-Pair-Share
Based on the problems we’ve done, list the steps in the diamond/box factoring method so that someone else can do a problem using only your steps.
2. Trade papers with your partner and use their steps to factor the following problem: x2 +4x -32.

12. Try w/ a partner 

13. You are up
6y2 – 13y – 5
1st•3rd
2nd
-30
-15 2
-13
(2y – 5)(3y + 1)

14. You can do it continued 2x -7 x 2x2 -7x 2x -7
a) b) 2x -7
-14 -5 x
2x x 2x +1
Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

15. Keep up the good work 3x +2 5x 15x2 10x -3x -2
a) b) 3x +2
-30 7 5x
15x2 10x
-3x -1
Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

16. TOO

17. Example 3 So what is another way we can solve this if we can’t factor?
How many solutions does this have? How can you tell?

18. Helpful X hints. + + + + - - + - - -
+ big
- small
- big
+ small + -

19. Mixed Review PRACTICE! GCF Difference of Squares Perfect Squares
Difference of Cubes
Grouping
Trinomials
x2 + 8x + 16

20. Homework
Factoring WS #3