Do all rational polynomial e.g $\frac{a}{b}x^n + \frac{c}{d}x^{n-1} + ... +\frac{e}{f}x + \frac{f}{g} = 0$ have a integer polynomial representation?
My thinking is:
$\frac{a}{b}x^2 + \frac{c}{d}x + \frac{e}{f} = 0$
$*bdf: adfx^2 + cbfx + ebd= 0$
Following on from that, what is considered the simplest form of a complex polynomial? is it something like $(a + bi)x^2 + (c + di)x + (e + fi) = 0$
Or is there a form that all complex polynomials can be expressed in?