Question Number 44541 by Yadavsantosh37941@gmail.com last updated on 01/Oct/18
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{the} \\ $$$$\mathrm{polynomial}\:{p}\left({y}\right)={y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{1}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:{y}−\mathrm{1}. \\ $$
Commented by $@ty@m last updated on 01/Oct/18
$${See}\:{Q}.\:{No}.\:\mathrm{40474} \\ $$
Answered by ajfour last updated on 01/Oct/18
$${p}\left({y}\right)\:=\:\left({y}−\mathrm{1}\right){q}\left({y}\right)+{r} \\ $$$${put}\:\:{y}=\mathrm{1}\:\: \\ $$$$\Rightarrow\:\:{p}\left(\mathrm{1}\right)\:=\:{r}\:=\:\mathrm{1}−\mathrm{3}+\mathrm{2}+\mathrm{1}\:=\:\mathrm{1}\:. \\ $$