Section 8.5 Day 2 Using the Distributive Property Algebra 1

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)

(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

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

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

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

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

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

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

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=−3 and 𝑑=5 The solutions of an equation are also called roots.

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

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

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=0 and 𝑏=5