Given any two polynomials in a single variable it is always possible to 
eliminate the variable and 
obtain a formula showing the relationship between the two polynomials. 
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Let <i>p</i>(<i>x</i>) = <i>x</i><sup>2</sup> + 2<i>x</i>  and <i>q</i>(<i>x</i>) = <i>x</i><sup>2</sup> + <i>x</i> + 1 then, using a method which does not depend on knowing 
the answer, show that the relationship between the polynomials is:
<p/>



<br clear="all" /><table border="0" width="100%"><tr><td>
<table align="center"><tr><td nowrap="nowrap" align="center">
<i>p</i><sup>2</sup> <font face="symbol">-</font
> 2<i>pq</i> + <i>q</i><sup>2</sup> + 3<i>p</i> <font face="symbol">-</font
> 4<i>q</i> + 3 = 0</td></tr></table>
</td></tr></table>