2. Factor the polynomial $x^{8}+4 x^{2}+4$ into the product of two quartic polynomials.
2. $\begin{aligned} & x^{8}+4 x^{2}+4=x^{8}+4 x^{2}+4+\left(4 x^{6}+8 x^{4}+4 x^{2}\right)-\left(4 x^{6}+8 x^{4}-4 x^{2}\right) \\ = & \left(x^{4}+2 x^{2}+2\right)^{2}-\left[2 x\left(x^{2}+1\right)\right]^{2} \\ = & \left(x^{4}+2 x^{3}+2 x^{2}+2 x+2\right)\left(x^{4}-2 x^{3}+2 x^{2}-2 x+2\right) .\end{aligned}$