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 \[{{x}^{3}}-3{{x}^{2}}+3x+7.\] |
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