Solving Polynomial Equations Section 4.5 beginning on page 190.

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Presentation transcript:

Solving Polynomial Equations Section 4.5 beginning on page 190

Solving By Factoring

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

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.

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.

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

The Irrational Conjugate Theorem

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

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