1. The Real Zeros of a Polynomial Function Section 5.2 Also Includes Section R.6 : Synthetic Division 1

2. Example: Division Algorithm 2

3. 29 = Dividend 7 = Divisor 4 = Quotient 1 = Remainder Is 7 a factor of 29? How can you tell? 3

4. The Division Algorithm for Polynomials 4

5. Remember … 5

6. 6

7. Remainder Theorem 7

8. Let’s try it ! 8

9. Exercise 12 Page 357 9

10. Section R.6 : Synthetic Division 10

11. 11

12. Begin by bringing down the leading coefficient. From now on, we will repeat steps 1 and 2 until finished. 12

13. Repeat steps 1 and 2 … 13

14. So what does this tell us? 14

15. Exercise 12 Page 62 15

16. Example 16

17. Exercise 10 Page 357 – True or False 17

18. How many real zeros are there? 18

19. 19

20. Exercise 8 Page 357 – True or False Every polynomial function of degree 3 with real coefficients has exactly three real zeros. 20

21. Rational Zeros Theorem 21

22. Exercise 26 Page 357 22

23. Your Turn : Exercise 32 Page 357 23

24. Exercise 100 Page 359 24

25. Rational Zero Theorem – Why use it? 25

26. 26

27. Factors of 2,310 27

28. Steps for finding real zeros of a polynomial 28

29. When a zero is found … 29

30. Example: Find the real zeros 30

31. Example continued … Step 3: Graph the polynomial. The red points are the possible rational zeros. Let’s test that point. The next slide shows the same graph but much larger. 31

32. 32

33. Example continued … 33

34. Example continued … 34

35. Exercise 70 Page 358 35

36. Using the calculator … 36