Wetzel 

Math 110

3.3 – Zeros of a Polynomial Function

Multiplicity –  the number of times a zero repeats

            Even –

            Odd –

** A polynomial of degree n will have n zeros.  (some may repeat)

The Rational Zero Theorem –

            Given a polynomial with integer coefficients, P(x), let p equal a factor of the constant term and q equal a factor of the leading coefficient.  Then is a possible zero of P(x).

            Ex.:

            1.)             Find all possible zeros.

Summarize -   Given a polynomial, P(x):

            1.)  Determine the number of zeros.

            2.)  List all possible zeros.

            3.)  Find a zero.

            4.)  Divide P(x) by the zero.

            5.)  Factor if possible.  If P(x) is still too large to factor, go back to step 3.

            6.)  Set each factor equal to zero and solve.

            Ex.:

            2.)              Solve.  Find all zeros.

HW:  6^th Ed.  p.321 #1-9odd, 41-51odd

          5^th Ed.  p.316  #1-9odd, 37-47odd