1. **State the problem:** Find the greatest common divisor (g.c.d) of the three polynomials $$x^2 + 3x - 4,$$ $$x^2 - 3x + 2,$$ and $$2x^2 - 5x + 3.$$\n\n2. **Factor each polynomial:**\n- $$x^2 + 3x - 4 = (x + 4)(x - 1)$$ because $(x + 4)(x - 1) = x^2 - x + 4x - 4 = x^2 + 3x - 4$.\n- $$x^2 - 3x + 2 = (x - 2)(x - 1)$$ because $(x - 2)(x - 1) = x^2 - x - 2x + 2 = x^2 - 3x + 2$.\n- $$2x^2 - 5x + 3 = (2x - 3)(x - 1)$$ because $(2x - 3)(x - 1) = 2x^2 - 2x - 3x + 3 = 2x^2 - 5x + 3$.\n\n3. **Identify common factors:**\n- The first polynomial factors as $(x + 4)(x - 1)$.\n- The second as $(x - 2)(x - 1)$.\n- The third as $(2x - 3)(x - 1)$.\nEach polynomial contains the factor $(x - 1)$.\n\n4. **Conclusion:** The g.c.d of the given polynomials is $$x - 1.$$