Respuesta :
Answer:
[tex]f(x)= x^2(x+9i)(x-9i)[/tex]
Step-by-step explanation:
[tex]f(x) = x^4 + 81x^2[/tex]
Lets factor GCF x^2
[tex]f(x) =x^2(x^2+81)[/tex]
Now factor out [tex]x^2+81[/tex]
LEts find out factors by solving, set the parenthesis =0 and solve for x
[tex]x^2+81=0[/tex]
Subtract 81 on both sides
[tex]x^2=-81[/tex]
take square root on both sides
[tex]x^2=\sqrt{-81}[/tex]
[tex]\sqrt{-1} =i[/tex]
[tex]x=i\sqrt{81}[/tex]
[tex]x=+-9i[/tex]
Two roots are [tex]x=-9i , x=+9i[/tex]
Factors are [tex](x+9i)(x-9i)[/tex]
So [tex]f(x)= x^2(x+9i)(x-9i)[/tex]
