question_answer

Out of the given responses, one of the factors of\[{{x}^{3}}-3{{x}^{2}}+3x+7\]is                                    [SSC (CGL) 2014]

A) \[{{x}^{2}}-4x+7\]

B) \[{{x}^{2}}+4x+7\]

C) \[{{x}^{2}}+4x-7\]                 

D) \[{{x}^{2}}-4x-7\]

Correct Answer: A

Solution :

Given expression,

\[f\,\,(x)={{x}^{3}}-3{{x}^{2}}+3x+7\]

By Hit and Trial,

Put       \[x=-\,\,1\]

\[\therefore \]\[f\,\,(-1)={{(-1)}^{3}}-3\,\,{{(-1)}^{2}}+3\,\,(-1)+7\]

\[=-\,\,1-3-3+7=0\]

So, \[x=-\,\,1\] or \[(x+1)\] is the factor of the expression.

Now, dividing expression by \[(x+1).\]

Hence, \[({{x}^{2}}-4x+7)\] is the factor of the expression \[{{x}^{3}}-3{{x}^{2}}+3x+7.\]