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Polynomial Advanced Properties - Rational Zeros and Descartes' Rule of Signs - Exercise 2

Use the Rational Zero Property and Descartes' Rule of Signs to list all the possible rational zeros of f(x) = 3x4 + 23x3 + 56x2 + 52x + 16.  Then use Synthetic Division and The Properties of Zeros to determine which, if any of the possible rational zeros is an actual zero.  When you find a zero, apply the Properties of Zeros to write the polynomial in reduced form and check possible zeros of the reduced polynomial. List all the zeros. Note that the justification is already given - no further justification is needed.

 

STATEMENT JUSTIFICATION
f(x) = 3x4 + 23x3 + 56x2 + 52x + 16 Given
Rational Zero Property
Descartes' Rule of Signs
Division Algorithm (Synthetic Division)
Properties of Zeros

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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