To factorize the expression \(m^3 - 2m^2 - m + 2\), we can use the rational root theorem to find the possible rational roots of the polynomial. The possible rational roots are ±1, ±2. Checking these values, we find that m = 1 is a root of the polynomial. This means that (m - 1) is a factor of the polynomial.

We can use synthetic division to divide the polynomial by (m - 1) to find the quadratic factor. The quadratic factor is:

\(m^2 - m - 2\)

This quadratic can be further factorized as:

(m - 2)(m + 1)

So, the complete factorization of the given expression is:

(m - 1)(m - 2)(m + 1)