Factoring polynomials over real and complex numbers

[NewtonianAlch]

Homework Statement

Factorise z$^{8}$ -15z$^{4}$ - 16 over the Complex numbers and Real numbers

The Attempt at a Solution

I factorised over the complex numbers, I'm not sure what they mean by over the real numbers.

Do I substitute z = (x + iy) and then do it by expanding and separating real from complex? I would have tried it at first, except these are powers to the 8, which seems like an unlikely method.

 

[tiny-tim]

Hi NewtonianAlch!

I factorised over the complex numbers, I'm not sure what they mean by over the real numbers.

over the complex numbers means that the factors have (possibly) complex coefficients (and will all be linear)

over the real numbers means that the factors have real coefficients (and will be either linear or quadratic)