Need some help with this math question?

Question

Factor the following polynomial function over the complex numbers: f(x) = x⁴ + 3x² − 4

 

-

Thanks to anyone who helps!

Answer 1

Let z = x^2

 

f(x) = x^4 + 3x^2 - 4

 

       = (x^2)^2 + 3x^2 - 4

 

 

f(z) = z^2 + 3z - 4

 

     = ( z     +     4 )( z     -       1   )

 

 

f(x) = (x^2 + 4)(x^2 - 1)

 

      = ( x  + 2i      )(   x - 2i      )(x + 1)(x-1)