Problem: One of the factors of x4+4x^{4}+4x4+4 is
Answer Choices:
A. x2+2x^{2}+2x2+2
B. x+1x+1x+1
C. x2−2x+2x^{2}-2x+2x2−2x+2
D. x2−4x^{2}-4x2−4
E. none of these Solution:
x4+4=(x4+4x2+4)−4x2x^{4}+4=\left(x^{4}+4 x^{2}+4\right)-4 x^{2} x4+4=(x4+4x2+4)−4x2
=(x2+2)2−(2x)2=(x2+2x+2)(x2−2x+2).=\left(x^{2}+2\right)^{2}-(2 x)^{2}=\left(x^{2}+2 x+2\right)\left(x^{2}-2 x+2\right) . =(x2+2)2−(2x)2=(x2+2x+2)(x2−2x+2).