<PRE><B>Question 442060</B>
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The problem with your question is that the answer is both yes and no.  I suspect you mean &lt;i&gt;Is it factorable over the &lt;u&gt;rational&lt;/u&gt;&lt;/i&gt; numbers, in which case the answer is no.   But all quadratic trinomials are factorable if you allow complex number factors.  A large subset of these are factorable over the real irrational numbers.  And only a tiny fraction of these are factorable over rational numbers.


The given quadratic actually has a pair of irrational factors:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12x^2\ +\ 39x\ -\ 20\ =\ \left(x\ -\ \left(\frac{-39\ +\ \sqrt{2481}}{24}\right)\right)\left(x\ -\ \left(\frac{-39\ -\ \sqrt{2481}}{24}\right)\right)] 
 



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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