1. Lesson 9.5 Factor 𝒙 𝟐 +𝒃𝒙+𝒄
Essential Question: How do you factor trinomials of the form 𝑥 2 +𝑏𝑥+𝑐?

2. Before we start…
Consider the binomials 𝑥+4 and 𝑥+2. What is the product? Look at the coefficient of x. How did you use 2 and 4 to get this coefficient? Look at the constant term. How did you use 2 and 4 to get this term?
Consider the binomials 𝑥−3 and 𝑥+1. What is the product? Look at the coefficient of x. How did you use -3 and 1 to get this coefficient? Look at the constant term. How did you use -3 and 1 to get this term?

3. What is factoring? 𝑥+3 𝑥+4 = 𝑥 2 +7𝑥+12
Undoing the multiplication of polynomials
𝑥+3 𝑥+4 = 𝑥 2 +7𝑥+12

4. How do you factor a trinomial in the form 𝑥 2 +𝑏𝑥+𝑐?
Find factors of the form 𝑥+𝑝 𝑥+𝑞 where 𝑝+𝑞=𝑏 and 𝑝𝑞=𝑐
You are looking for factors of c that add/subtract to get b.

5. How do you know what signs to use?
𝑥 2 +𝑏𝑥+𝑐
𝑥 2 +𝑏𝑥−𝑐
Positive means the same signs
Negative means the opposite signs
𝒙+𝒑 𝒙+𝒒
𝒙+𝒑 𝒙−𝒒
𝒙−𝒑 𝒙−𝒒
𝒙−𝒑 𝒙+𝒒

6. Factor
𝑥 2 +11𝑥+18

7. Factor
𝑥 2 +3𝑥+2

8. Factor
𝑛 2 −6𝑛+8

9. Factor
𝑦 2 +2𝑦−15

10. Factor
𝑥 2 −4𝑥+3

11. Factor
𝑚 2 +𝑚−20

12. Factor
𝑥 2 +8𝑥+12

13. Factor
𝑎 2 +7𝑎+10

14. Factor
𝑤 2 +6𝑤−16

15. How do you solve polynomial equations?
Set the equation equal to 0.
Factor the polynomial.
Set each factor equal to 0.
Solve each factor.

16. Solve
𝑥 2 +3𝑥=18

17. Solve
𝑠 2 −2𝑠=24

18. Solve
𝑥 2 −3𝑥=28

19. Solve
𝑎 2 +5𝑎=50

20. How do you factor trinomials of the form 𝑥 2 +𝑏𝑥+𝑐?

21. Ticket Out the Door
Factor 𝑥 2 +6𝑥+5