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Question Number 128157 by naka3546 last updated on 04/Jan/21

Let  P(x)  is  monic  polynomial  function  such  that                  [P(2x)]^2  = P(4x) + 16P(x^2 )  P(x) =  ?

$${Let}\:\:{P}\left({x}\right)\:\:{is}\:\:{monic}\:\:{polynomial}\:\:{function}\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[{P}\left(\mathrm{2}{x}\right)\right]^{\mathrm{2}} \:=\:{P}\left(\mathrm{4}{x}\right)\:+\:\mathrm{16}{P}\left({x}^{\mathrm{2}} \right) \\ $$$${P}\left({x}\right)\:=\:\:? \\ $$

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