1. Using the Distributive Property (GCF)
8.5 Notes
Using the Distributive Property (GCF)

2. Warm-up
List the factors of each of the numbers. Then circle the greatest (biggest) one they have in common.
1) 15, 20, ) 21, 49, ) 8, 24, 4

3. Vocab!
Factoring

4. GCF Basics
1. Ask yourself if the number will divide into the other numbers. a. If it does, that’s your GCF! b. If it doesn’t, keep looking. Think of (or list) factors of the __________ number. c. Of those factors, find the number that will divide into all the numbers.

5. Example 1 – Find the GCF
a) 6, 18, 14 b) 24, 3, 12 c) 8, 24, 28

6. GCF of a Variable Take the number of variables possible.
2. If even one term does a variable, don’t include any variables in your GCF.

7. Example 2 – Find the GCF
a) x6 + x2 + x7 b) 1 + x4 + x9 c) x + x4 + x3 - x2

8. Things to Remember! Make sure your polynomial is in first.
If your leading coefficient is , make your negative.

9. Example 3 – Factoring
a) 15x + 25x b) 4x2y2 + 2x3y3 + 8xy4

10. Example 3 cont.
c) 9p3 + 6p6 – d) 12xy + 24xy2 – 30x2y4

11. Additional Examples Find the GCF of the following polynomials:
4p4 + 12p 2) 18d6 – 6d2 + 3d ) –33x x2
4) 5x3 – 25x2 – 35x 5) 4x ) 75x4y + 3x2

12. Additional Examples
7) -3w4 + 21w3 8) 24t7  60t3 + 48t4  36t 9) 14𝑡 4 −35𝑡−21 10) 8𝑑 4 𝑞 4 + 4𝑑 3 𝑞 𝑑 2 𝑞 3 11) 5𝑐 3 −25 𝑐 2 +10𝑐 12) 15 𝑦 3 +6 𝑦 2 −21𝑦

13. Additional Examples
13) 5𝑥 𝑦 𝑥 2 𝑦 14) 3 𝑥 4 𝑧 3 −24 𝑥 2 𝑧 15) −10 𝑦 4 −2 𝑦 2 16) 35 𝑎 3 −28 𝑎 2 17) 32𝑥−48 𝑥 2 18) 35𝑥𝑦−60 𝑥 2

14. Additional Examples
19) 3 𝑚 2 +24𝑚 ) 4𝑥 4 +4𝑥− ) 2 𝑡 3 +2 𝑡 2 −12𝑡

15. Warm-up
Factor out the GCF in the following problems 1) 3x – 6 2) 5x2 – 10x 3) 12x3 + 6x2 – 4x

16. Vocab!
Zero Product Property

17. Example 1 – Solve
Solve each equation using the zero product property. Check each solution. a) (x – 2)(4x – 1) = 0 b) 12y2 = 4y

18. Example 1 cont.
c) (s – 3)(3s + 6) = 0 d) 40x2 – 5x = 0

19. Example 2 - Application
A football is kicked into the air. The height of the football can be modeled by the equation h = –16x2 + 48x, where h is the height reached by the ball after x seconds. Find the values of x when h = 0.

20. Example 3 – Application
Juanita is jumping on a trampoline in her back yard. Juanita’s jump can be modeled by the equation h = –14t2 + 21t, where h is the height of the jump in feet at t seconds. Find the values of t when h = 0.