Math 112 Section 2.5 Theorems About Zeros of Polynomial Functions

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Math 112 Section 2.5 Theorems about Zeros of Polynomial Functions

Finding Polynomials with Given Zeros:

Example 1: Find a polynomial of degree 3 given the zeroes: -3, 4, -5

Nonreal Zeros: If is a zero of , then so is .

Example 2: Find a polynomial of degree 3 given the zeroes: -1, 2 – 3i

Irrational Zeros: If is a zero of , then so is if b is not a perfect square.

Example 3: If , 1 + 4i are zeros of a polynomial, find the other zeros and a polynomial of lowest degree with these zeros.

Rational Zeros Theorem: Possible Factors of .

:

Example 4: List the possible factors of

Factors of 15: è Possible factors of f(x) are

Factors of 1:

Example 5: List the possible factors of . Then eliminate some based on the graph.