[tex]\displaystyle\\x^4+10x^2+25=\\\\=x^4+5x^2+5x^2+25=\\\\=(x^4+5x^2)+(5x^2+25)=\\\\=x^2(x^2+5)+5(x^2+5)=\\\\=(x^2+5)(x^2+5)=\\\\=\left(x^2+\left(\sqrt{5}\right)^2\right)\left(x^2+\left(\sqrt{5}\right)^2\right)=\\\\=\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)=\\\\=\Big(x+i\sqrt{5}\Big)\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)=\\\\=\boxed{\Big(x+i\sqrt{5}\Big)^2\Big(x-i\sqrt{5}\Big)^2}[/tex]
