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Question Number 129514 by abdurehime last updated on 16/Jan/21

The polynomial p(x)is divided by x−4 and x+2 the remainders are 8 and 4 respectivily. find the remainder when p(x)is divided by (x−4)(x+2)

$$\mathrm{The}\:\mathrm{polynomial}\:\mathrm{p}\left(\mathrm{x}\right)\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}−\mathrm{4}\:\mathrm{and}\:\mathrm{x}+\mathrm{2}\:\mathrm{the}\:\mathrm{remainders}\:\mathrm{are}\:\mathrm{8}\:\mathrm{and}\:\mathrm{4}\:\mathrm{respectivily}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{p}\left(\mathrm{x}\right)\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}+\mathrm{2}\right) \\ $$$$ \\ $$

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!

$${please}\:{don}'{t}\:{write}\:{the}\:{whole}\:{post}\:{in} \\ $$$${a}\:{single}\:{line}!\:{try}\:{to}\:{use}\:{line}\:{breack}! \\ $$$${this}\:{will}\:{make}\:{your}\:{post}\:{better} \\ $$$${readable}\:{for}\:{other}\:{people}! \\ $$

Answered by liberty last updated on 16/Jan/21

p(x): (x−4)(x+2) give remainder   r(x)=(((x−4)/(−2−4)))×4+(((x+2)/(4+2)))×8   r(x)= ((16−4x+8x+16)/6)=((4x+32)/6)=((2x+16)/3)

$$\mathrm{p}\left(\mathrm{x}\right):\:\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}+\mathrm{2}\right)\:\mathrm{give}\:\mathrm{remainder}\: \\ $$$$\mathrm{r}\left(\mathrm{x}\right)=\left(\frac{\mathrm{x}−\mathrm{4}}{−\mathrm{2}−\mathrm{4}}\right)×\mathrm{4}+\left(\frac{\mathrm{x}+\mathrm{2}}{\mathrm{4}+\mathrm{2}}\right)×\mathrm{8} \\ $$$$\:\mathrm{r}\left(\mathrm{x}\right)=\:\frac{\mathrm{16}−\mathrm{4x}+\mathrm{8x}+\mathrm{16}}{\mathrm{6}}=\frac{\mathrm{4x}+\mathrm{32}}{\mathrm{6}}=\frac{\mathrm{2x}+\mathrm{16}}{\mathrm{3}} \\ $$

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