1. 7.4 Solving factored polynomials

2. What We Will Learn Use Zero Product Property
Factor using Greatest Common Factor (GCF)
Solve by factoring story problems

3. Needed Vocab.
Factored form: when polynomial written as a product of its factors
Zero Product Property: setting factors of a polynomial equal to zero to solve
Roots: solution to a polynomial equation
Repeated roots: when two or more answers are the same

4. Exs. 1 and 2 Solve using Zero Product Property
2𝑥(𝑥 − 4) = 0
2𝑥=0
2𝑥 2 = 0 2
𝑥=0
𝑥−4=0
+4 +4
𝑥=4
Answers then 0 and 4
Set each factor = to 0
2𝑥+7 2𝑥−7 =0
2𝑥+7= 𝑥−7=0
−7 −
2𝑥=−7 2𝑥=7
2𝑥 2 = − 𝑥 7 = 7 2
𝑥= −7 2 𝑥= 7 2

5. Exs. 1 and 2 Cont. Your Practice 𝑥+1 2 𝑥−3 2𝑥−2
𝑥−1 2 =0
𝑥−1 2 means 𝑥−1 𝑥−1
𝑥−1=0 𝑥−1=0
𝑥= 𝑥=1
Repeated root
Your Practice
𝑥 𝑥−3 2𝑥−2
𝑎𝑛𝑠𝑤𝑒𝑟𝑠 𝑎𝑟𝑒 −1, −1, 3, 1 or -1, 3, 1

6. Ex. 3 Taking Out Greatest Common Factor
4𝑥 𝑥 3
GCF: 4𝑥 3
4𝑥 4 4𝑥 𝑥 3 4𝑥 3
4𝑥 3 𝑥+6
8𝑦 2 −24𝑦
GCF: 8𝑦
8𝑦 2 8𝑦 − 24𝑦 8𝑦
8𝑦 𝑦−3
GCF: biggest number, letter, or combination of both that all terms have in common
To find:
1. look for biggest number if there is one
2. look for same variable(s) if there is one
Use lowest exponent for GCF
To factor out:
1. Put GCF in front of ( )
2. divide all terms by GCF and put answer in ( )

7. Ex. 3 cont. Factor: 5𝑧 2 +12𝑧 GCF: 𝑧 Your Practice Factor:
5𝑧 2 𝑧 + 12𝑧 𝑧
𝑧 5𝑧+12
6𝑥 3 +18
GCF: 6 6𝑥
6 𝑥 3 +3
Your Practice
Factor:
20𝑥 𝑥 2
GCF: 10𝑥 2
20𝑥 𝑥 𝑥 𝑥 2
10𝑥 2 2𝑥+3

8. Ex. 4 Solve by Factoring 2𝑥 2 =−8𝑥 +8𝑥 +8𝑥 Steps 2𝑥 2 +8𝑥=0
+8𝑥 +8𝑥
2𝑥 2 +8𝑥=0
GCF: 2𝑥
2𝑥 2 2𝑥 + 8𝑥 2𝑥
2𝑥 𝑥+4 =0
2𝑥=0 𝑥+4=0
𝑥= −4 −4
𝑥=0 𝑎𝑛𝑑 𝑥=−4
Steps
1. get = to zero
2. find GCF
3. take out GCF
4. set factors = to zero
5. solve

9. Your Practice 3𝑛=0 3𝑛 3 = 0 3 𝑛=0 Solve 2𝑛−5=0 6𝑛 2 =15𝑛 +5 +5
2𝑛=5
2𝑛 2 = 5 2
𝑛= 5 2
So answers are 0 and 5/2 or 2.5
Solve
6𝑛 2 =15𝑛
−15𝑛 −15𝑛
6𝑛 2 −15𝑛=0
GCF: 3𝑛
6𝑛 2 3𝑛 − 15𝑛 3𝑛
3𝑛 2𝑛−5 =0