| 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 \[{{x}^{3}}-3{{x}^{2}}+3x+7.\] |
You need to login to perform this action.
You will be redirected in
3 sec
