1. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least degree with given roots. Identify all of the roots of a polynomial equation. Objectives

2. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Find the zeros of the polynomial function P(x) = x 3 – 4x 2 – 4x + 16 Warm Up: Happy Friday!!!!

3. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Write the simplest polynomial function with the given zeros. Example 1 –2, 2, 4

4. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra

5. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Example 2: Finding All Roots of a Polynomial Solve x 4 – 3x 3 + 5x 2 – 27x – 36 = 0 by finding all roots. The polynomial is of degree 4, so there are exactly four roots for the equation.

6. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Solve x 4 + 4x 3 – x 2 +16x – 20 = 0 by finding all roots. The polynomial is of degree 4, so there are exactly four roots for the equation. Check It Out! Example 2

7. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Example 3: Writing a Polynomial Function with Complex Zeros Write the simplest function with zeros 2 + i and 1.

8. Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Lesson Quiz: Part I Write the simplest polynomial function with the given zeros. 1. 2, –1, 1 2. 0, –2, 3. 2i, 1, –2 4. Solve by finding all roots. x 4 – 5x 3 + 7x 2 – 5x + 6 = 0 x 3 – 2x 2 – x + 2 x 4 + 2x 3 – 3x 2 – 6x x 4 + x 3 + 2x 2 + 4x – 8 2, 3, i,–i