Answer:
[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]
Step-by-step explanation:
We are given that an expression
[tex]x^4+10x^2+25[/tex]
We have to find the factorize the expression completely over the cmplex number.
[tex](x^2+5)^2[/tex]
Using identity [tex](a+b)^2=a^2+b^2+2ab[/tex]
[tex](x^2+5)(x^2+5)[/tex]
Substitute each factor equal to zero.
[tex]x^2+5=0[/tex] ,[tex]x^2+5=0[/tex]
[tex]x^2=-5[/tex]
[tex]x=\pm \sqrt{-5}=\pm i \sqrt 5[/tex]
[tex]x=i\sqrt 5[/tex] and [tex]x=-i\sqrt 5[/tex]
[tex]x-i\sqrt 5=0[/tex] and [tex]x+i\sqrt 5=0[/tex]
The factor of second term is also same
Therefore, the factors of the expression completely is given by
[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]
