DESCARTES’ RULE OF SIGNS - Central Bucks School District

[Pages:2]Pre-Calculus/Trig 3 UNIT 2: Polynomial Functions ? SECTION 5 WORKSHEET

Name: _________________________ Date: _________________________

DESCARTES' RULE OF SIGNS

Directions: State the number of possible positive and negative real zeros for each function.

1.) () = 34 + 20 - 32

2.) () = 54 - 422 + 49

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

3.) () = 43 - 122 - 5 + 1

4.) () = 24 - 33 +

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

5.) () = 24 + 32 - 54

6.) () = 6 - 64

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

7.) () = 96 - 35 + 334 - 113 + 182 - 6

8.) () = 646 - 1

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

9.) () = 25 + 44 + 93 + 182 - 35 - 70

10.) () = 65 - 44 - 633 + 422 + 147 - 98

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

11.) () = 166 - 324 - 252 + 50

12.) () = 7 - 64

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

13.) () = 86 + 93 + 1

14.) () = 276 + 263 - 1

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

# of possible positive real zeros: _____________ # of possible negative real zeros: _____________

Directions: Use your knowledge of properties of polynomial functions to determine all zeros WITHOUT a calculator. 15.) () = -43 + 152 - 8 - 3

a.) Determine the end behavior of ().

- () _____

() _____

b.) Determine the possible number of turning points of ().

# of possible turning points:

_____

c.) Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of ().

# of possible positive real zeros: _________________________

# of possible negative real zeros: _________________________

d.) Use synthetic division to test for rational zeros.

FACTORS: ________________________________

ZEROS:

________________________________

-intercept(s): ________________________________

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