Question Number 129514 by abdurehime last updated on 16/Jan/21
$$\mathrm{The}\:\mathrm{polynomial}\:\mathrm{p}\left(\mathrm{x}\right)\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}−\mathrm{4}\:\mathrm{and}\:\mathrm{x}+\mathrm{2}\:\mathrm{the}\:\mathrm{remainders}\:\mathrm{are}\:\mathrm{8}\:\mathrm{and}\:\mathrm{4}\:\mathrm{respectivily}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{p}\left(\mathrm{x}\right)\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}+\mathrm{2}\right) \\ $$$$ \\ $$
Commented by mr W last updated on 16/Jan/21
$${please}\:{don}'{t}\:{write}\:{the}\:{whole}\:{post}\:{in} \\ $$$${a}\:{single}\:{line}!\:{try}\:{to}\:{use}\:{line}\:{breack}! \\ $$$${this}\:{will}\:{make}\:{your}\:{post}\:{better} \\ $$$${readable}\:{for}\:{other}\:{people}! \\ $$
Answered by liberty last updated on 16/Jan/21
$$\mathrm{p}\left(\mathrm{x}\right):\:\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}+\mathrm{2}\right)\:\mathrm{give}\:\mathrm{remainder}\: \\ $$$$\mathrm{r}\left(\mathrm{x}\right)=\left(\frac{\mathrm{x}−\mathrm{4}}{−\mathrm{2}−\mathrm{4}}\right)×\mathrm{4}+\left(\frac{\mathrm{x}+\mathrm{2}}{\mathrm{4}+\mathrm{2}}\right)×\mathrm{8} \\ $$$$\:\mathrm{r}\left(\mathrm{x}\right)=\:\frac{\mathrm{16}−\mathrm{4x}+\mathrm{8x}+\mathrm{16}}{\mathrm{6}}=\frac{\mathrm{4x}+\mathrm{32}}{\mathrm{6}}=\frac{\mathrm{2x}+\mathrm{16}}{\mathrm{3}} \\ $$