Exercise 1.

Find all rational zeros of the polynomial

displaymath30

Answer.

Rational zeros of the form tex2html_wrap_inline34 satisfy the following: p divides the constant coefficient 6; q divides the leading coefficient 1. The choices for p are: tex2html_wrap_inline46 , the only choices for q are: tex2html_wrap_inline50 . Thus p/q is one of the following:

displaymath32

Check each of these 8 candidates by plugging the values into the polynomial:

P(1)=8, P(-1)=0, P(2)=0, P(-2)=-100, P(3)=0, P(-3)=-600, P(6)=3108, P(-6)=-13320. Thus the rational zeros of the polynomial P(x) are tex2html_wrap_inline72 .

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Helmut Knaust
Tue Jun 24 12:39:39 MDT 1997

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