A) \[(x+1)\]
B) \[(x-1)\]
C) \[(3x+7)\]
D) \[(2x-3)\]
Correct Answer: B
Solution :
Let the expressions be \[P(x)\] and \[Q(x)\]. \[\therefore \] \[P(x)+Q(x)=5{{x}^{2}}-x-4\] ?.(i) \[P(x)-Q(x)={{x}^{2}}+9x-10\] ?..(ii) On adding, \[2P(x)=5{{x}^{2}}+{{x}^{2}}-x+9x-4-10\] \[=6{{x}^{2}}+8x-14\] \[\therefore \] \[P(x)=3{{x}^{2}}+4x-7\] From equation (i). \[Q(x)=5{{x}^{2}}-x-4-3{{x}^{2}}-4x+7\] \[=2{{x}^{2}}-5x+3\] Again. \[P(x)=3{{x}^{2}}+4x-7\] \[=3{{x}^{2}}+7x-3x-7\] \[=x(3x+7)-1(3x+7)\] \[=(3x+7)\,(x-1)\] \[Q(x)=2{{x}^{2}}-5x+3\] \[=2{{x}^{2}}-2x-3x+3\] \[=2x(x-1)-3(x-1)\] \[=(2x-3)\,(x-1)\] \[\therefore \] HCF \[=x-1\]
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