factoring syntax

[sonic widget]

Hello, just confused about the wording of problems such as ‘factor 8x^3 -27 over the real numbers’

i understand all the factoring, just not sure if im understanding ‘over the reals’ correctly.

as i understand:

‘over the imiginaries’: factor up to the point of i’s

‘over the reals’: factor to the point of sqrt’s

‘factor’: factor but no square roots or i’s

Am i correct?

[south breach]

Just “factor” doesn’t really specify what number system you’re using. Just assume whatever would be more natural.

It wouldn’t really make sense to only factor to the point of rational numbers, ignoring irrational roots.