A) \[(x+3)\]
B) \[(x-3)\]
C) \[(x+3)(x-2)\]
D) \[(x-1)\]
Correct Answer: A
Solution :
Here, LCM \[=({{x}^{3}}-7x+6)\] or \[{{x}^{3}}-7x+6=(x+3)(x-2)(x-1)\] By synthetic division as \[(x-1)\]is a factor, so \[1\,\,\left| \!{\nderline {\, \begin{matrix} 1 & 0 & -7 & 6 \\ {} & 1 & 1 & -6 \\ 1 & 1 & -6 & 0 \\ \end{matrix} \,}} \right. \] \[q\,\,(x)={{x}^{2}}+x-6=(x+3)(x-2)\] \[p\,\,(x)=(x+3)(x-1)\] \[HCF=\frac{p\,\,(x)\times q\,\,(x)}{LCM}=\frac{(x+3)(x-1)\times (x+3)(x-2)}{(x-1)(x-2)(x+3)}\] \[=(x+3)\]You need to login to perform this action.
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