A) \[\left( x+3 \right)\left( x+1 \right)\]
B) \[\left( {{x}^{2}}-1 \right)\left( x+2 \right)\left( x-3 \right)\]
C) \[\left( x-1 \right)\left( x-2 \right)\left( x-3 \right)\]
D) \[\left( {{x}^{2}}-1 \right)\left( x+2 \right)\left( x+3 \right)\]
Correct Answer: B
Solution :
(b) (i) \[{{x}^{2}}-1={{x}^{2}}-{{\left( -1 \right)}^{2}}=(x-1)(x+1)\] (ii) \[{{x}^{2}}-4x+3={{x}^{2}}-3x-x+3\] \[=x\left( x-3 \right)-1\left( x-3 \right)=\left( x-3 \right)\left( x-1 \right)\] (iii)\[{{x}^{2}}+3x+2={{x}^{2}}+2x+x+2\] \[=x\left( x+2 \right)+1\left( x+2 \right)=\left( x+2 \right)\left( x+1 \right)\] \[LCM=\left( x-1 \right)\left( x+1 \right)\left( x+2 \right)\left( x-3 \right)\]
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