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The Real Zeros of a Polynomial Function

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Presentation on theme: "The Real Zeros of a Polynomial Function"— Presentation transcript:

1 The Real Zeros of a Polynomial Function
Section 4.2 The Real Zeros of a Polynomial Function Copyright © 2013 Pearson Education, Inc. All rights reserved

2 Use the Remainder and Factor Theorems.
Objectives Use the Remainder and Factor Theorems. Use the Rational Zeros theorem to list the potential rational zeros of a polynomial function. Find the real zeros of a polynomial function. Solve polynomial equations Use the theorem for bounds on zeros. Use the Intermediate Value Theorem. Copyright © 2013 Pearson Education, Inc. All rights reserved

3 Copyright © 2013 Pearson Education, Inc. All rights reserved

4 Copyright © 2013 Pearson Education, Inc. All rights reserved

5 The remainder is –1. The remainder is 5.
Copyright © 2013 Pearson Education, Inc. All rights reserved

6 Copyright © 2013 Pearson Education, Inc. All rights reserved

7 By the factor theorem, x + 1 is a factor of f(x).
By the factor theorem, x – 1 is not a factor of f(x). Copyright © 2013 Pearson Education, Inc. All rights reserved

8 Copyright © 2013 Pearson Education, Inc. All rights reserved

9 Copyright © 2013 Pearson Education, Inc. All rights reserved

10 Factors of the constant
Factors of the leading coefficient Copyright © 2013 Pearson Education, Inc. All rights reserved

11 Since f is a polynomial of degree 3, there are at most three real zeros.
Copyright © 2013 Pearson Education, Inc. All rights reserved

12 Copyright © 2013 Pearson Education, Inc. All rights reserved

13 Step 1: There are at most 4 real zeros.
Copyright © 2013 Pearson Education, Inc. All rights reserved

14 Copyright © 2013 Pearson Education, Inc. All rights reserved

15 Copyright © 2013 Pearson Education, Inc. All rights reserved

16 BOUND Copyright © 2013 Pearson Education, Inc. All rights reserved

17 Copyright © 2013 Pearson Education, Inc. All rights reserved

18 Copyright © 2013 Pearson Education, Inc. All rights reserved

19 Copyright © 2013 Pearson Education, Inc. All rights reserved

20 Copyright © 2013 Pearson Education, Inc. All rights reserved

21 Homework: 4.2 page 209 #11, 13, 21, 27, 33, 39, 45, 47, 53, 63, 71, 75

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