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Problem Of The Week #463 April 13th 2021

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anemone

MHB POTW Director
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Feb 14, 2012
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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,894
Congratulations to castor28 for his correct solution (Cool) , which you can find below:
We have:
\begin{align*}
(x+1)(x+2)(x+5) - 36x &= x^3 + 8x^2 - 19x + 10\\
&= (x+10)(x-1)^2
\end{align*}
and this is non-negative for all positive $x$ (in fact, for all $x\ge-10$).
 
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