A) \[{{x}^{4}}-{{x}^{3}}+{{x}^{2}}-4x+8\]
B) \[{{x}^{3}}+{{x}^{2}}-4x+8\]
C) \[{{x}^{4}}-{{x}^{3}}+{{x}^{2}}+4x-8\]
D) \[{{x}^{4}}-{{x}^{3}}-{{x}^{2}}+4x-8\]
Correct Answer: A
Solution :
Required expression \[=({{x}^{4}}+2{{x}^{2}}-3x+7)-({{x}^{3}}+{{x}^{2}}+x-1)\] \[={{x}^{4}}+2{{x}^{2}}-3x+7-{{x}^{3}}-{{x}^{2}}-x+1\] \[={{x}^{4}}-{{x}^{3}}+2{{x}^{2}}-{{x}^{2}}-3x-x+7+1\] \[={{x}^{4}}+\frac{1}{4}{{x}^{3}}-\frac{3}{2}{{x}^{2}}+\frac{3}{4}x\]
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