1. Section 8.6-8.7 Day 3 Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0
Algebra 1

2. Learning Targets Factor trinomials in the form 𝑎 𝑥 2 +𝑏𝑥+𝑐
Solve algebraic equations of the form 𝑎 𝑥 2 +𝑏𝑥+𝑐=0

3. Multiple Variables Example 1
Factor 𝑥 2 −14𝑥𝑦−51 𝑦 2
𝑎∙𝑐=−51 𝑦 2
𝑏=−14𝑦
Answer: (𝑥+3𝑦)(𝑥−17𝑦)

4. Multiple Variables Example 2
Factor 𝑎 2 +10𝑎𝑏−39 𝑏 2
𝑎∙𝑐=−39 𝑏 2
𝑏=10𝑏
Answer: (𝑎+13𝑏)(𝑎−3𝑏)

5. 2 Step Factoring – Level 1 Example 3
GCF: 4
4( 𝑎 2 +8𝑎−48)
Answer: 4(𝑎−4)(𝑎+12)

6. 2 Step Factoring: Level 1 Example 4
GCF: 2
2(−4 𝑥 2 +19𝑥+30)
Answer: 2(4𝑥+5)(−𝑥+6)

7. 2 step Factoring: Level 2 Example 6
GCF: 4𝑥
4𝑥(3 𝑥 2 −17𝑥+20)
Answer: 4𝑥(3𝑥−5)(𝑥−4)

8. Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Example 5
Solve 6 𝑥 3 −51 𝑥 2 +90𝑥=0
3𝑥 2 𝑥 2 −17𝑥+30 =0
3𝑥 𝑥−6 2𝑥−5 =0
Answer: 𝑥=0, 𝑥=6, 𝑥= 5 2

9. Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Example 7
Solve 3 𝑛 5 −6 𝑛 4 =105 𝑛 3
Rewrite: 3 𝑛 5 −6 𝑛 4 −105 𝑛 3 =0
GCF: 3 𝑛 3
3 𝑛 3 𝑛 2 −2𝑛−35 =0
3 𝑛 3 𝑛−7 𝑛+5 =0
Answer: 𝑛=0, 𝑛=7, 𝑛=−5

10. Solving 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Example 8 (PG 512: #4)
A person throws a ball upward from a 506-foot tall building. The ball’s height ℎ in feet after 𝑡 seconds is given by the equation ℎ= −16 𝑡 2 +48𝑡+506. The ball lands on a balcony that is 218 feet above the ground. How many seconds was it in the air?
218=−16 t 2 +48t+506
0=−16 𝑡 2 +48𝑡+288
0=−16 𝑡 2 −3𝑡+18 =−16(𝑡−6)(𝑡+3)
𝑡=6 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

11. Problem 1
Factor 𝑥 2 +9𝑥+20
Answer: (𝑥+5)(𝑥+4)

12. Problem 2
Solve 2 𝑥 2 +22𝑥=−20
Answer: 2 𝑥+10 (𝑥+1)
𝑥=−10 and 𝑥=−1

13. Problem 3
Solve 2 𝑥 2 −3𝑥=20
Answer: 𝑥=4, 𝑥=− 5 2