1. Warm Up Find the GCF 1) 56, 26 2) 144x5wz3, 36x3z2m
Factor Completely 3) 18z4 + 21z3 – 9z2 4) 3xy + 21x – 2y – 14

2. Divisibility Rules

3. Homework 

4. Standard Form: ax2 + bx + c
Factoring
Standard Form:
ax2 + bx + c

5. Factoring is the opposite of multiplying:
(x +7)(x + 3) =
x2 + 10x + 21
Factoring

6. there are many methods we can use to get to the same answer I am going to show you two ways You decide which one you like

7. Method 1…
We have to find a number that multiplies to the “c” term whose factors add to the “b” term
(x +7)(x + 3) =
x2 + 10x + 21
7 • 3 = 21
7 + 3 = 10
Some people like to organize this using an X-box,
and not the gaming system

8. First and Last Coefficients
Factor the x-box way
y = ax2 + bx + c
Product
ac=mn
First and Last Coefficients
Now let’s practice
Finding the m and n terms n m
Middle
b=m+n
Sum

11. Now let’s Factor!!!

12. First and Last Coefficients
Examples
Factor. 1. x2 + 4x – 12
y = ax2 + bx + c
Product
ac=mn
-12 4
First and Last Coefficients 6 -2 n m
Middle
b=m+n
Sum
Solution: x2 + 4x – 12 = (x + 6)(x - 2)

13. First and Last Coefficients
Examples continued
y = ax2 + bx + c
2. x2 - 9x + 20
Product
ac=mn 20 -9
First and Last Coefficients n m
Middle
b=m+n
Sum
Solution: x2 - 9x + 20 = (x - 4)(x - 5)

14. Method 2…
“Undoing” the Box
x2 - 7a + 6

15. x2 – 3x - 28

16. x + x2

17. d2 – 6d – 27

18. 2x2 + 6x + 4

19. x2 – 9

20. Think-Pair-Share
Based on the problems we’ve done, list the steps for factoring 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.
Make sure your partner uses the same method as you!!!!

21. Trying out the Steps
If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partner’s paper back to him.
Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner.
Try using the steps again to factor: x2 - x - 56.

22. You Try!- Choose your own method
Factor the expression: x2 + 7x + 10

23. You Try!
Factor the expression: x2 – 2x – 24

24. You Try!
Factor the expression: x2 – 15x + 26

25. You Try!
Factor the expression: x2 – 6x – 27

26. You try!!!
Factor the expression: x2 + 9x + 14