A) \[{{x}^{3}}-2{{x}^{2}}+x+2\]
B) \[{{x}^{3}}-2{{x}^{2}}+x-2\]
C) \[{{x}^{3}}+2{{x}^{2}}+x+2\]
D) \[{{x}^{3}}-2{{x}^{2}}-x-2\]
Correct Answer: C
Solution :
Product of the polynomials \[=\]Product of their \[LCM\] and\[HCF\] \[\therefore \] \[f(x).g(x)=LCM\times HCF\] or \[g(x)=\frac{1\cdot ({{x}^{2}}-4)({{x}^{4}}-1)}{{{x}^{3}}-2{{x}^{2}}-x+2}\] \[=\frac{(x-2)(x+2)(x-1)(x+1)({{x}^{2}}+1)}{{{x}^{2}}(x-2)-(x-2)}\] \[=(x+2)({{x}^{2}}+1)\] \[={{x}^{3}}+2{{x}^{2}}+x+2\]
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