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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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