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1. Lesson Video 6.7 “What are we trying to accomplish?” Algebra 2 2013-14 Example by Mrs. G Give It a Try

2. Lesson 6.7 • Use The Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function. • Find all zeros of a polynomial function. Objective Video Example by Mrs. G Give It a Try

3. Video YouTube sturmmath Objective Video Example by Mrs. G Give It a Try

4. Example by Mrs. G GENERAL STATEMENT: In general, when all real and imaginary solutions are counted (with all repeated solutions counted individually), an nth-degree polynomial has exactly n solutions. Similarly, an nth-degree polynomial function has exactly n zeros. Click to continue. Objective Video Example by Mrs. G Give It a Try

5. Example by Mrs. G Ex 1: Finding the Number of Solutions/Zeros • Equations have solutions, whereas functions have zeros, they are basically the same thing. • How many zeros does the function have? • Since it is a 4th degree function, there are 4 zeros. Click to continue. Objective Video Example by Mrs. G Give It a Try

6. Example by Mrs. G • Find all the zeros of • Start by making a list of possible rational zeros: • Test the rational zeros using synthetic division: -1 1 -2 1 -8 -12 -1 3 -4 12 1 -3 4 -12 0 reduced polynomial (now cubic) Click to continue. Objective Video Example by Mrs. G Give It a Try

7. Example by Mrs. G • Find all the zeros of • Continue to test the rational zeros using synthetic division and the reduced polynomial until your result is a quadratic: -1 1 -2 1 -8 -12 -1 3 -4 12 1 -3 4 -12 0 3 0 12 1 0 4 0 3 reduced polynomial (quadratic) Click to continue. Objective Video Example by Mrs. G Give It a Try

8. Example by Mrs. G • Find all the zeros of • Factored form: • Set each factor = 0: • Zeros: Click to continue. Objective Video Example by Mrs. G Give It a Try

9. Give It a Try • Find the number of zeros of the polynomial function. • Find all the zeros of the function. Bring your work and answer to our next class! Objective Video Example by Mrs. G Give It a Try