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I came across this in homework but I'm interested in the general example, say $ax+bx^{-1}+c.$

Jack Pan
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    What about factoring $ax^2+b+cx$, does this look more promising? – Did Jun 21 '16 at 20:02
  • Remember that the general way of factorising is to find zeros. So if you equate $ax+bx^{-1} +c = 0$, then you can multiply with $x$ on both sides and obtain a polynomial, which this have been marked a duplicate of. – Nicky Mattsson Jun 21 '16 at 20:53

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In fact if you write it like $\frac 1 x ( x ^ 2 + 2 x + 1 )$, the problem is just factoring a polynomial.