Exercise 5.

Show the following: If a polynomial has integer coefficients and its leading coefficient is 1, then all of its rational zeros are in fact integers.

Answer.

By the Rational Zero Test, a rational zero of the form tex2html_wrap_inline33 must satisfy that q divides the leading coefficient 1; consequently tex2html_wrap_inline37 , so

displaymath31

an integer.

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Helmut Knaust
Tue Jun 24 12:51:02 MDT 1997

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