Zeros of Polynomial Functions

Zeros of Polynomial Functions - Each time you find a zero...

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3.3: Zeros of Polynomial Functions A polynomial function P of degree n has at most n zeros, where each zero of multiplicity k is counted k times. The Rational Zero Theorem If P ( x ) = a n x n + a n -1 x n -1 + . . . + a 1 x + a 0 has integer coefficients ( a n 0) and p q is a rational zero (in lowest terms) of P , then œ p is a factor of the constant term a 0 œ q is a factor of the leading coefficient a n . Use the Rational Zero Theorem to list all possible rational zeros for each function. P ( x ) = 2 x 3 + x 2 - 25 x + 12 P ( x ) = x 2 - 8 x + 16 P ( x ) = 4 x 4 - 12 x 3 - 3 x 2 + 12 x - 7

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Steps for Finding the Zeros of a Polynomial Function with Integer Coefficients 1. Gather general information. If the polynomial is of degree n , the number of distinct zeros is at most n . 2. Check suspects. Use the Rational Zero Theorem to list all possible zeros. Then use synthetic division to test numbers in your list. 3. Work with the reduced polynomials.

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Unformatted text preview: Each time you find a zero, you will have a reduced polynomial leftover. œ If a reduced polynomial is of degree 2, use factoring or the quadratic formula to find its zeros. œ If a reduced polynomial is of degree 3 or higher, repeat steps (1) and (2). Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicty. P ( x ) = x 3 + 6 x 2 + 3 x- 10 Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicty. P ( x ) = 3 x 3 + 11 x 2- 6 x- 8 Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicty. P ( x ) = x 3- 3 x- 2 Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicty. P ( x ) = x 4- 5 x 2- 2 x...
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This test prep was uploaded on 04/13/2008 for the course MATH 2412 taught by Professor Matroy during the Spring '08 term at Alamo Colleges.

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Zeros of Polynomial Functions - Each time you find a zero...

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