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Module 2                                                                                                                             30

For the following polynomials:

a.  State the degree and the sign of the leading coefficient.  Then use the

    information to determine the left and right behavior of the graph (the end

    behavior).

b.  List all of the real zeros with their multiplicity and state the behavior at the x-axis

    of each zero (crosses or touches).

c.  Based on parts (a) and (b), draw a rough sketch of the graph without using a

    calculator.     

d.  Check part (c) with a graphing calculator.

Example:  p(x) = 3(x + 4)3(x + 1)(x – 5)2,

   Zeros   Multiplicity   Crosses/Touches

   degree                 6           –4          3          Crosses

    sign                positive       –1          1          Crosses

    End behavior     ↑  ↑         5          2Touches

1.  f(x) = (x + 3)3(x – 2)2(x – 4)

2.  g(x) = –x(x – 5)(x + 2)3                

3.  h(x) = –3(x – 1)2(x + 1)2         

4.  j(x) = 6(x + 5)(x + 4) 2(x – 1)4(x – 3)2

5.  j(x) = –x3 + 4x                          

6.  k(x) = x3 – 4x2      

Finding Real Zeros of Polynomial Functions  

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