Problem: One of the factors of x4+2x2+9x^{4}+2 x^{2}+9x4+2x2+9 is:
Answer Choices:
A. x2+3x^{2}+3x2+3
B. x+1x+1x+1
C. x2−3x^{2}-3x2−3
D. x2−2x−3x^{2}-2 x-3x2−2x−3
E. none of these Solution:
x4+2x2+9=(x4+6x2+9)−(4x2)x^{4}+2 x^{2}+9=\left(x^{4}+6 x^{2}+9\right)-\left(4 x^{2}\right)x4+2x2+9=(x4+6x2+9)−(4x2)
=(x2+3)2−(2x)2=(x2−2x+3)(x2+2x+3)=\left(x^{2}+3\right)^{2}-(2 x)^{2}=\left(x^{2}-2 x+3\right)\left(x^{2}+2 x+3\right) =(x2+3)2−(2x)2=(x2−2x+3)(x2+2x+3)
∴(E)\therefore(\mathrm{E})∴(E) is the correct choice.