Question

How do you factor `10m^3n^2-15m^2n+25m`?

Answer 1

`10m^3n^2-15m^2n+25m = 5m(2m^2n^2-3mn+5)`

To see that this does not factor further, let `p=mn`.

Then `2m^2n^2-3mn+5=2p^2-3p+5`

If this had linear factors, then it would factorise as `(2p-1)(p-5)` or `(2p-5)(p-1)` in order to get the coefficient of `p^2` and the constant term correct. Neither of these works.