A) \[x\]
B) \[{{x}^{3}}\]
C) \[14+{{x}^{2}}\]
D) \[{{x}^{5}}\]
Correct Answer: D
Solution :
\[\left| \begin{matrix} 4+{{x}^{2}} & -6 & -2 \\ -6 & 9+{{x}^{2}} & 3 \\ -2 & 3 & 1+{{x}^{2}} \\ \end{matrix} \right|\] \[=(4+{{x}^{2}})[(1+{{x}^{2}})(9+{{x}^{2}})-9]\] \[+6[-6(1+{{x}^{2}})+6]-2[-18+2(9+{{x}^{2}})]\] \[=(4+{{x}^{2}})(9+9{{x}^{2}}+{{x}^{2}}{{x}^{4}}-9)\] \[+6(-6-6{{x}^{2}}+6)-2(-18+18+2{{x}^{2}})\] \[=(4+{{x}^{2}})(10{{x}^{2}}+{{x}^{4}})-36{{x}^{2}}-4{{x}^{2}}\] \[=40{{x}^{2}}+4{{x}^{4}}+10{{x}^{4}}+{{x}^{6}}-40{{x}^{2}}\] \[=14{{x}^{4}}+{{x}^{6}}\] \[={{x}^{4}}({{x}^{2}}+14)\] Which is not divisible by \[{{x}^{5}}\].
You need to login to perform this action.
You will be redirected in
3 sec
