I am dealing with an issue for which I do not find answer on the Internet. When I factorize a polynomial, I can get this structure:
$ (x-a)(x-b)(x-c)^2 $
But sometimes I have seen others like: $ k(x-a)(x-b)(x-c)^2 $
Where $k$ is any real number. What does it mean? I know it is related with the coefficient of the root with the highest algebraic multiplicity but I don't get to understand it.
It could be $\frac{1}{3}(x-1)(x-2)$ but never $(x-1)(x-2)+\frac{1}{3}$ isn't it? Why? Thank you a lot :)