Zeros of Polynomial Functions

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online