1. Section 8.5 Day 2 Using the Distributive Property
Algebra 1

2. GCF Puzzle Problem 1 Fill in the blanks knowing the final answer.
(5___)(___𝑥+6)=45 𝑥 2 +30𝑥
5𝑥 9𝑥+6 =45 𝑥 2 +30𝑥
Correct Answer: 15𝑥(3𝑥+2)

3. (2𝑥𝑦)(__+__+__)=6 𝑥 2 𝑦 7 −8 𝑥 8 𝑦 2 +2𝑥𝑦
GCF Puzzle Problem 2
Fill in the blanks knowing the final answer.
(2𝑥𝑦)(__+__+__)=6 𝑥 2 𝑦 7 −8 𝑥 8 𝑦 2 +2𝑥𝑦
2𝑥𝑦 3𝑥 𝑦 6 −4 𝑥 7 𝑦+1 =6 𝑥 2 𝑦 7 −8 𝑥 8 𝑦 2 +2𝑥𝑦

4. Factoring Binomials: Example 1
1. Find GCF of both terms
GCF =9𝑦
2. Pull out the GCF and write the remainder
9𝑦(3𝑦+2)

5. Factoring Binomials: Example 2
GCF=3𝑥 𝑦 3
3𝑥 𝑦 3 (2𝑥𝑦−3)

6. Factoring Polynomials: Example 3
1. GCF
GCF: 2𝑎𝑏
2. Factor out GCF
2𝑎𝑏(−2𝑎−4𝑏+1)

7. Factoring Polynomials: Example 4
GCF: 𝑢∙𝑡=𝑢𝑡
𝑢𝑡(7𝑢𝑡+21𝑡−1)

8. Factoring Polynomials: Example 5
GCF: 3 𝑟 2 𝑡
3 𝑟 2 𝑡(6𝑟𝑡+2𝑡−2)

9. Zero Product Property
If the product of two factors is 0, then at least one of the factors must be 0.
____ ∙_____=0
Option 1:
# ∙0=0
Option 2:
0∙#=0
Option 3:
0∙0=0

10. Zero Product Property: Example 6
Solve 2𝑑+6 3𝑑−15 =0
By ZPP, you can set each factor equal to zero and solve.
2𝑑+6=0 3𝑑−15=0
2𝑑=−6 3𝑑=15
𝑑=− and 𝑑=5
The solutions of an equation are also called roots.

11. Zero Product Property: Example 7
Solve 4𝑥 8𝑥−6 =0
4𝑥=0 8𝑥−6=0
𝑥=0 8𝑥=6
𝑥=0 and 𝑥= 6 8 = 3 4
𝑥=0 & 𝑥= 3 4 are the solutions/roots of the equation

12. Zero Product Property: Example 8
Solve 𝑐 2 =3𝑐
Get everything to one side. Need to have "=0" !
𝑐 2 −3𝑐=0 (solve)
𝑐 𝑐−3 =0 (factor)
𝑐=0 𝑐−3=0
𝑐=0 and 𝑐=3

13. Zero Product Property: Example 9
Solve 8 𝑏 2 =40𝑏
1. Solve 8 𝑏 2 −40𝑏=0
2. Factor 8𝑏 𝑏−5 =0
3. ZPP 8𝑏=0 𝑏−5=0
𝑏= and 𝑏=5