y= x^3 - x^2
y=(x-2)^3 - (x-2)^2
these are 2 functions for which i am trying to find the roots
just with the second question...
(x-2)^3 - (x-2)^2
sometimes it helps to give the common factor, in this case (x-2) a letter say for example z. this just makes factorizing a little easier.
for example:
let (x-2) = z
so the new equation (if we sub in z whenever we see a (x-2) becomes:
z^3 - z^2
so this factorized becomes
z^2(z-1)
and now sub in for z (x-2)
(x-2)^2((x-2)-1)
which is equal to:
(x-2)^2(x-3)
hope that helps a little for in the future!