A) \[\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}-1+x \right)\]
B) \[\left( {{x}^{2}}-1-x \right)\left( {{x}^{2}}-1-x \right)\]
C) \[\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}-1-x \right)\]
D) \[({{x}^{2}}+1-x)({{x}^{2}}+1+x)\]
Correct Answer: D
Solution :
(d) \[{{x}^{4}}+{{x}^{2}}+1\] \[{{x}^{4}}+{{x}^{2}}+1={{x}^{4}}+{{x}^{2}}+1\text{+}{{\text{x}}^{2}}-{{x}^{2}}\] \[=({{x}^{4}}+2{{x}^{2}}+1)-{{x}^{2}}\] \[={{\left( {{x}^{2}}+1 \right)}^{2}}-{{x}^{2}}=\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}+1+x \right)\]
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