Sections 4.2 and 4.3 – Zeros of Polynomial Functions ...

Sections 4.2 and 4.3 ? Zeros of Polynomial Functions Complex Numbers

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Sections 4.2 and 4.3 ? Find the Zeros of Polynomial Functions and Graph

Recall from section 4.1 that the end behavior of a polynomial function is the same as the EB

of the leading term

() =

1) For each polynomial function do the following: a) Give the leading term and end behavior b) Find ALL the zeros and classify them as rational-real, irrational-real, imaginary, complex. c) Identify the x-intercepts d) Write the polynomial as a product of linear factor e) Sketch a complete graph ? some can be done without the calculator ? which ones?

1. () = (2 - 4)(2 - 5)( - 3)

2. () = -(2 + 4)( - 5)

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Sections 4.2 and 4.3 ? Zeros of Polynomial Functions

Objective: Sketching complete graphs of polynomial functions (if possible) using the end behavior and the real zeros. 2) For each polynomial function do the following: a) Give the leading term and end behavior b) Find ALL the zeros and classify them as rational-real, irrational-real, imaginary, complex. c) Identify the x-intercepts d) Write the polynomial as a product of linear factor e) Sketch a complete graph ? some can be done without the calculator ? which ones? 1. () = (2 - 2)(2 - 2 + 2)

2. () = -0.5(2 + 1)(2 - 2 + 2)

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Sections 4.2 and 4.3 ? Zeros of Polynomial Functions ? Related Theorems

Now we'll be dealing with polynomial functions of the form

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Sections 4.2 and 4.3 ? Finding Zeros of Polynomial Functions

Finding all zeros of a Polynomial Function when it is given on the form 3) For the polynomial function () = 33 + 82 - 7 - 12. To make this process easier and faster we will not use the method outlined on the book. Follow the steps outlined below. a) How many complex zeros does the polynomial have? b) Enter the function in the Y= of the calculator c) How many real zeros (x-intercepts) does the function have? Find them by using the ZERO feature in the calculate menu. Classify them as rational-real, irrational-real, imaginary, complex. d) Write the function in factored form:

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