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Solving Polynomial Equations Section 4.5 beginning on page 190.

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Presentation on theme: "Solving Polynomial Equations Section 4.5 beginning on page 190."— Presentation transcript:

1 Solving Polynomial Equations Section 4.5 beginning on page 190

2 Solving By Factoring

3 Finding Zeros and Graphing The zeros are 2 and -2. Both factors are raised to an even power, so the graph will touch the x-axis at those points. This is an even degree polynomial with a negative leading coefficient so the ends both go down. The y-intercept is -32

4 The Rational Root Theorem This theorem gives a starting point for factoring some higher degree polynomials. We will often list the possible factors, and then test them to find one factor and go from there.

5 Using the Rational Root Theorem Factors of 20: 1,2,4,5,10,20 Factors of 1: 1 List the possible solutions: Test the possible solutions using synthetic division until you find one that works.

6 Continued…. Lastly, factor completely using the result of the synthetic division.

7 The Irrational Conjugate Theorem

8 Using Zeros to Write a Polynomial Step 1: Write in factored form. Step 2: Regroup the terms (notice how this is a special product) Step 3: Multiply everything out and simplify

9 Monitoring Progress

10

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