Question Number 61261 by Jmasanja last updated on 31/May/19
$${for}\:{polynomial}\:{p}\left({x}\right),{the}\:{value}\:{of}\: \\ $$$${p}\left(\mathrm{3}\right)\:{is}\:−\mathrm{2}.{which}\:{of}\:{the}\:{following}\: \\ $$$${must}\:{be}\:{true}\:{about}\:{p}\left({x}\right)? \\ $$$$\left({a}\right){x}−\mathrm{5}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({b}\right){x}−\mathrm{2}{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({c}\right){x}+\mathrm{2}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({d}\right){the}\:{reminder}\:{when}\:\:{p}\left({x}\right)\:{is}\:{divide} \\ $$$${d}\:{by}\:{x}−\mathrm{3}\:{is}\:−\mathrm{2} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Answered by tanmay last updated on 31/May/19
![p(x)=(x−3)q(x)+R(x) p(3)=(3−3)q(3)+R(3) p(3)=R(3)=−2 [remainder=−2]](https://www.tinkutara.com/question/Q61263.png)
$${p}\left({x}\right)=\left({x}−\mathrm{3}\right){q}\left({x}\right)+{R}\left({x}\right) \\ $$$${p}\left(\mathrm{3}\right)=\left(\mathrm{3}−\mathrm{3}\right){q}\left(\mathrm{3}\right)+{R}\left(\mathrm{3}\right) \\ $$$${p}\left(\mathrm{3}\right)={R}\left(\mathrm{3}\right)=−\mathrm{2}\:\:\:\left[{remainder}=−\mathrm{2}\right] \\ $$