1. Factoring Using the Distributive Property Chapter 9.2

2. Factoring using Distribution Remember the distributive property:

3. Factoring using Distribution Today we are going to use the distributive property in reverse! This is a different type of factoring

4. Factoring using Distribution Example 1: Use the distributive property to factor: In order to factor this, we need to find the GCF (greatest common factor) Factor each number

5. Factoring using Distribution Find the GCF

6. Factoring using Distribution We are now going to take the GCF out of each number We can divide each number by 4 Now we have a different equation, so to keep it the same we have to keep the 4 with it

7. Factoring using Distribution If we distributed the 4 we would end up with the same equation we started with So our answer is

8. Factoring using Distribution Factor the following: 1. 24x + 18 4. 13x + 23 3. -25 – 40x 5. 18x + 72 2. 60x + 210

9. Factoring using Distribution Factor the following: 1. 24x + 18 4. 13x + 23 3. -25 – 40x 5. 18x + 72 2. 60x + 210 6(4x + 3) -5(5 – 8x) 18(x + 4) Not Factorable 30(2x + 7)

10. Factoring using Distribution Example 2: Factor Find the GCF

11. Factoring using Distribution Take 3x out of the original problem Check your answer

12. Factoring using Distribution Factor the following: 1. 24x 2 + 15x 4. 13x + 52x 3 3. 21x – 39x 3 2. 80x 4 + 200x 2 5. 28x 3 y 3 + 98x 2 y

13. Factoring using Distribution Factor the following: 1. 24x 2 + 15x 4. 13x + 52x 3 3. 21x – 39x 3 5. 28x 3 y 3 + 98x 2 y 2. 80x 4 + 200x 2 3x(8x + 5) 3x(7 – 13x 2 ) 14x 2 y(2x y 2 + 7) 40x 2 (2x 2 + 5) 13x(1 + 4x 2 )

14. Factoring using Distribution Example 2: Factor Find the GCF on the left side

15. Factoring using Distribution Take 3x out of the original problem Now we have to solve the problem

16. Factoring using Distribution Remember, if x*y = 0 then either x or y has to be zero Therefore either 3x or (2x – 3) has to equal 0

17. Factoring using Distribution Set each one equal to zero and solve separately

18. Factoring using Distribution So for these problems, there can be 2 answers for x If you plug in either one, the equation should equal zero

19. Factoring using Distribution Plug in x = 0 This works!

20. Factoring using Distribution Plug in 3/2 for x This works too!

21. Factoring using Distribution Factor the following: 1. 3x 2 + 12x = 0 4. 52x 2 + 13x 3 = 0 3. 12x(x – 9) = 0 5. 9x 2 = 27x 2. x 2 = 7x

22. Factoring using Distribution Factor the following: 1. 3x 2 + 12x = 0 4. 52x 2 + 13x 3 = 0 3. 12x(x – 9) = 0 5. 9x 2 = 27x 2. x 2 = 7x 0 and -4 0 and 9 0 and 3 0 and 7 0 and -4

23. Factoring using Distribution Example 3: Factor the following Once again, find the GCF of all three numbers

24. Factoring using Distribution Take 2x 2 out of the original equation

25. Factoring using Distribution Factor each equation 1. 6x 3 + 15x 2 – 9x 4. 16x 3 + 32x 2 + 24x 3. 18x + 36x 2 – 81x 3 5. 70x 3 y 3 + 105x 2 y – 175xy 2 2. 12x 4 + 48x 3 + 36x 2

26. Factoring using Distribution Factor each equation 1. 6x 3 + 15x 2 – 9x 4. 16x 3 + 32x 2 + 24x 3. 18x + 36x 2 – 81x 3 5. 70x 3 y 3 + 105x 2 y – 175xy 2 2. 12x 4 + 48x 3 + 36x 2 3x(2x 2 + 5x – 3) 9x(2 + 4x – 9x 2 ) 35xy(2x 2 y 2 + 3x – 5y) 12x 2 (x 2 + 4x + 3) 8x(2x 2 + 4x + 3)

27. Factoring using Distribution Factor the following 1. -9x – 3 4. 16x 2 – 80x = 0 3. 24x 2 y 3 – 84xy 2 2. 12x 4 + 18x 3 5. 45x 3 + 63x 2 + 9x

28. Factoring using Distribution Factor the following 1. -9x – 3 4. 16x 2 – 80x = 0 3. 24x 2 y 3 – 84xy 2 2. 12x 4 + 18x 3 -3(3x + 1) 12xy 2 (2xy – 7) 6x 3 (2x + 3) 0 and 5 5. 45x 3 + 63x 2 + 9x 9x(5x 2 + 7x + 1)