A) \[{{x}^{2}}+5x+4\]
B) \[{{x}^{2}}-5x+4\]
C) \[{{x}^{2}}+4x+5\]
D) \[{{x}^{2}}-4x+5\]
Correct Answer: A
Solution :
| [a] \[LCM=({{x}^{2}}+6x+8)(x+1)\] or \[\text{(}x+4)\,(x+2)\,(x+1)\] \[HCF=(x+1),\] One expression \[={{x}^{2}}+3x+2\] or \[(x+1)(x+2)\] As we know that Product of two expression \[=\text{ }LCM\times HCF\] \[(x+1)(x+2)\times 2nd\] expression \[=(x+4)(x+2)(x+1)(x+1)\] 2nd expression \[=\frac{(x+4)(x+2)(x+1)(x+1)}{(x+1)(x+2)}\] \[=(x+4)(x+1)=\text{ }{{x}^{2}}+4x+x+4\] \[={{x}^{2}}+5x+4\] |
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