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Question Number 176846 by Ar Brandon last updated on 27/Sep/22

$$m\in \mathbb{Z}$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{leading}\mathrm{coefficient}\mathrm{of}\mathrm{the}\mathrm{polynomial}$$$$\mathrm{P}\left(x\right)=4x^{\frac{13}{m-5}}-6x^{25-2m}+4x^{13}+5x^{10}-4?$$

Answered by mr W last updated on 27/Sep/22

$$\frac{13}{m-5}=+integer\Rightarrow m=18or6$$$$25-2m=+integer\Rightarrow m=6$$$$\mathrm{P}\left(x\right)=4x^{13}-6x^{13}+4x^{13}+5x^{10}-4$$$$\mathrm{P}\left(x\right)=2x^{13}+5x^{10}-4$$$$\Rightarrow leadingcoeff.is2.$$

Commented by Ar Brandon last updated on 28/Sep/22

Thanks Sir

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