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Question Number 188082 by Shrinava last updated on 25/Feb/23

$$\mathrm{P}\left(\mathrm{x}\right)\mathrm{is}\mathrm{a}\mathrm{polynomial}$$$$\mathrm{If}\mathrm{P}({\mathrm{x}}^2+1)={6\mathrm{x}}^4-{\mathrm{x}}^2+5$$$$\mathrm{Find}\mathrm{P}({\mathrm{x}}^2-1)=?$$

Answered by cortano12 last updated on 25/Feb/23

$$\mathrm{let}{\mathrm{x}}^2=\mathrm{u}-1\Rightarrow \mathrm{P}\left(\mathrm{u}\right)=6{(\mathrm{u}-1)}^2-(\mathrm{u}-1)+5$$$$\Rightarrow \mathrm{P}\left(\mathrm{x}\right)=6{(\mathrm{x}-1)}^2-\mathrm{u}+6$$$$\Rightarrow \mathrm{P}({\mathrm{x}}^2-1)=6{({\mathrm{x}}^2-2)}^2-({\mathrm{x}}^2-1)+6$$$$$$

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