can all parablas be expressed in factered form
(explain with examples)
It depends on what you want. You can always put a parabola into the vertex form:
if you would consider that factored.
However, if you are given , where a, b, and c are integers, and want to write it as
then the answer is, in general, no if you are talking about integer d, e, f, and g.
There are not even any real numbers d, e, f, and g such that the right hand side factors.