# Polynomials and Rational Functions : Synthetic Division and Descarte's Rule of Signs

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1.USE DESCARTES` RULE OF SIGNS TO DETERMINE THE POSSIBLE NUMBER OF POSITIVE REAL ZEROS OF THE FUNCTION.

f(x)=3x cube-4x squared-2x-4

ANSWER: A.3 or 1 B.1 C.2 or 0 D.5, 3, OR 1

2.USE SYNTHETIC DIVISION TO COMPLETE THE INDICATED FACTORIZATION:x cube-7x-6=(x-3)( )

3.USE SYNTHETIC DIVISION TO COMPLETE THE INDICATED FACTORIZATION: x forth -4x cube-19x squared +106x-120 = (x-3)( )

4.USE SYNTHETIC DIVISION TO DETERMINE WHICH OF THE FOLLOWING

POLYNOMIALS IS NOT A FACTOR OF : x cube + 5x squared-4x-20

5. EXAMINE THE LEAD TERM AND DETERMINE THE FAR-LEFT AND FAR-RIGHTBEHAVIOR OF THE GRAPH OF THE POLYNOMIAL FUNCTION.

N(x)=2+8x squared-4x cube

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##### Solution Summary

Polynomials are investigated using synthetic division and Descarte's rule of signs. A graph is also drawn.

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Solution:

1.

According to DESCARTES` RULE OF SIGNS, there is one sign change. This number ...

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