I'm reading one theorem in the book called Contemporary Abstract Algebra by Gallian, and here's what puzzles me somewhat:
If $f(x) = (x-a)^mg(x) = (x-b)^m\phi(g(x))$ then how does the author deduce that the multiplicity of $b$ is at least $m$? Why not less than $m$ or equal to $m$?
Thank you for clarifying this for me.
