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

Example: Division Algorithm 2

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

The Division Algorithm for Polynomials 4

Remember … 5

6

Remainder Theorem 7

Let’s try it ! 8

Exercise 12 Page 357 9

Section R.6 : Synthetic Division 10

11

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

Repeat steps 1 and 2 … 13

So what does this tell us? 14

Exercise 12 Page 62 15

Example 16

Exercise 10 Page 357 – True or False 17

How many real zeros are there? 18

19

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

Rational Zeros Theorem 21

Exercise 26 Page

Your Turn : Exercise 32 Page

Exercise 100 Page

Rational Zero Theorem – Why use it? 25

26

Factors of 2,310 27

Steps for finding real zeros of a polynomial 28

When a zero is found … 29

Example: Find the real zeros 30

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

Example continued … 33

Example continued … 34

Exercise 70 Page

Using the calculator … 36