1. Lesson 9.8 Factor Polynomials Completely
Essential Question: How do you factor polynomials completely?

2. Before we start… 𝑦 1 =4 𝑥 2 −12 𝑦 2 =4 𝑥 2 −3
𝑦 1 =4 𝑥 2 −12 𝑦 2 =4 𝑥 2 −3
𝑦 3 =𝑥 𝑥−3 +5 𝑥−3 𝑦 4 = 𝑥−3 𝑥+5

3. Factor
2𝑥 𝑥+4 −3 𝑥+4

4. Factor
3 𝑦 2 𝑦−2 +5 𝑦−2

5. Factor
𝑥 𝑥−2 + 𝑥−2

6. Factor
4𝑦 𝑦−3 +5 𝑦−3

7. Factor by Grouping
Polynomials with four terms can sometimes be factored by grouping terms.
Group the terms into pairs and look for common factors.

8. How do you factor by grouping?
Group the terms.
Factor each group.
Find the common factor of the two new terms.

14. Factor Completely
When we factor an expression, the result can sometimes be factored further.
A polynomial that is factored completely is written as a product of unfactorable polynomials.

15. How do you factor completely?
Factor out a GCF.
Factor the remaining polynomial.
Trinomials
Difference of squares
Perfect square trinomials
By grouping

16. Factor completely
𝑛 2 +2𝑛−1

17. Factor completely
4𝑥 3 −44 𝑥 2 +96𝑥

18. Factor completely
50 ℎ 4 −2 ℎ 2

19. Factor completely
3𝑥 3 −12𝑥

20. Factor completely
𝑚 3 −2 𝑚 2 −8𝑚

21. Factor completely
2𝑥 2 −4𝑥−30

22. Factor completely
−𝑥 2 +10𝑥−21

23. Factor completely
𝑏 3 −5 𝑏 2 −4𝑏+20

24. Solve
𝑤 3 −8 𝑤 2 +16𝑤=0

25. Solve
𝑥 3 −25𝑥=0

26. Solve
𝑐 3 −7 𝑐 2 +12𝑐=0

27. How do you factor polynomials completely?

28. Ticket Out the Door
Factor
𝑥 3 + 𝑥 2 +2𝑥+2