Cubics- Roots?

Question

Cubics - What form will the equations take (factorised) if they have one root, two roots, three roots?

Answer 1

1 root: a(x - r)^3
has the single root r with multiplicity 3

2 roots: a(x - r)(x - s)^2
(r != s) has the roots r and s with multiplicity 2

3 roots: a(x - r)(x - s) (x - t)
(r != s != t) has roots r, s, t

Answer 2

a is not zero

a(x-r1)=0

a(x-r1)(x-r2)=0

a(x-r1)(x-r2)(x-r3)=0