Question Number 104275 by mubarakagulamhusain last updated on 20/Jul/20
$$\mathrm{The}\:\mathrm{HCF}\:\mathrm{of}\:\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right)\:\mathrm{and}\: \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}+\mathrm{2}\right)\:\:\mathrm{is} \\ $$
Commented by 1549442205PVT last updated on 20/Jul/20
$$\mathrm{you}\:\mathrm{can}\:\mathrm{tell}\:\mathrm{me}\:\mathrm{what}\:\mathrm{is}\:\mathrm{brief}\:\mathrm{word}\:''\mathrm{HCF}''? \\ $$$$ \\ $$
Commented by Rasheed.Sindhi last updated on 20/Jul/20
$${Highest}\:{Common}\:{Factor} \\ $$
Answered by Rasheed.Sindhi last updated on 20/Jul/20
$$\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right) \\ $$$$\underset{−} {\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}+\mathrm{2}\right)=\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)} \\ $$$$\:{Common}\:{factors}:\left({x}−\mathrm{1}\right),\:\left({x}+\mathrm{2}\right) \\ $$$$\:{Highest}\:{C}.\:{Factors}:\left({x}−\mathrm{1}\right)\left({x}+\mathrm{2}\right) \\ $$$$\:{OR}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} +{x}−\mathrm{2} \\ $$