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$-\frac12n^4-n^3+n^2+\frac32n$ in the form $\frac14n^2(n+1)^2$

I dont see how this is possible however its a question i was set, surely $\frac32n$ will never be able to be placed in that format as it is all multiplied by $n^2$?

Sonny Da Silva-Peters
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    Please give us the exact wording of the question you were set. – Gerry Myerson Jun 21 '17 at 07:16
  • the whole question is asked here: https://math.stackexchange.com/questions/2330733/given-that-sumn-r-2r3-can-be-written-in-the-form-an4bn3cn2dn however i thought i could simplify it as people don't want to read too much so i posted a new one i will delete whichever doesn't get replied to – Sonny Da Silva-Peters Jun 21 '17 at 07:18
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    Doesn't match for $,n=-1,$, so it can't match in general. – dxiv Jun 21 '17 at 07:21
  • As I suspected, no one is asking you to express that quartic in that form. You made a mistake in the algebra. The values you got for $a,\dots,e$ are not consistent with the last of the five equations in the five unknowns at that earlier question. – Gerry Myerson Jun 21 '17 at 07:24
  • oh okay, thanks, ill try read through it again and fix it (i already did but must of missed it) – Sonny Da Silva-Peters Jun 21 '17 at 07:31

2 Answers2

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The easiest coefficient to check is that of $n^4$. On the right hand side it is $\frac14$. Not the same on the left, right?

Actually, your method is pretty easy too, and correct.

Matt Samuel
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For large $n$:

$-\frac12n^4-n^3+n^2+\frac32n <0$.

For all $n$:

$\frac14n^2(n+1)^2>0$

Fred
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