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

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

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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 Lets 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. Lets 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