1. Lesson 9.6 Factor 𝒂𝒙 𝟐 +𝒃𝒙+𝒄
Essential Question: How do you factor trinomials of the form 𝑎𝑥 2 +𝑏𝑥+𝑐?

2. Before we start…
Consider 2 𝑥 2 +9𝑥+9 Consider the binomials 2𝑥+9 and 𝑥+1. Multiply the first two terms. Multiply the last two terms. Find the middle terms now.
Consider 2 𝑥 2 +9𝑥+9 Consider the binomials 2𝑥+3 and 𝑥+3. Multiply the first two terms. Multiply the last two terms. Find the middle terms now.

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 𝑎𝑥 2 +𝑏𝑥+𝑐?
You are looking for factors of a and c that add/subtract to get b.

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

6. Factor
2𝑥 2 −7𝑥+3

7. Factor
3𝑛 2 +14𝑛−5

8. Factor
3𝑡 2 +8𝑡+4

9. Factor
4𝑠 2 −9s+5

10. Factor
2𝑥 2 −13𝑥+6

11. Factor
4𝑎 2 +11𝑎−3

12. Factor
−3𝑤 2 −13𝑤−4

13. Factor
−4𝑥 2 +12𝑥+7

14. Factor
−2𝑦 2 −5𝑦−3

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
2𝑐 2 −11𝑐+5=0

17. Solve
2𝑦 2 +𝑦−10=0

18. Solve
9𝑤 2 +3𝑤−2=0

19. Solve
2𝑥 2 −3𝑥=35

20. Solve
8𝑠 2 −2𝑠=3

21. Solve
6𝑥 2 −5𝑥=14

22. Solve
7𝑎 2 +2𝑎=5

23. How do you factor trinomials of the form 𝑎𝑥 2 +𝑏𝑥+𝑐?

24. Ticket Out the Door
Factor 2𝑥 2 −7𝑥+3