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Module 2                                                                                                                             32

1.  For the function  

   a.  State the degree of the polynomial

   b.  State the number of zeros the polynomial function will have.

   c.  Use the Rational Zero Theorem to list all of the possible rational zeros.

   d.  Use your calculator to determine which numbers in the list of rational zeros

        are probable rational zeros.

   e.  Use synthetic division to verify one rational zero.  

   f.  Use synthetic division or other algebraic methods to find all remaining

       zeros.  List all of the zeros of the polynomial function.

2.  For the function

   a.  State the degree of the polynomial

   b.  State the number of zeros the polynomial function will have.

   c.  Given that is a zero, find all remaining zeros.  List all of the zeros of the

        polynomial function.

3.  Given a cubic polynomial function p(x) = ax3 + bx2 + cx + d, (a, b, c, d ≠ 0), answer the

    following questions.  Justify each answer.

    a.  How many x-intercepts can there be?

    b.  Does the degree of this polynomial function guarantee any x-intercepts?

    c.  Will the graph pass through the origin?

    d.  Could the graph “touch” the x-axis in two different places?

    e.  Identify the end behavior of the graph.

    f.  If it is known that one zero is real and another zero is imaginary, what can be

        determined about the remaining zeros?

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