To solve a third order recurrence relation with a characteristic polynomial factored as (x-1)^3, the characteristic root r=1 has a multiplicity of 3. The general solution will take the form of a linear combination of terms involving powers of the root and polynomial factors, specifically: a_0 + a_1*n + a_2*n^2, where a_0, a_1, and a_2 are constants determined by initial conditions. The next step involves using the initial conditions to find these constants. This approach effectively addresses the recurrence relation.