Choice A is the correct answer. To solve the quadratic equation $x^2 - 5x + 6 = 0$ by factoring:

1. Find two numbers that multiply to +6 and add to -5. The numbers are -2 and -3.
2. Write in factored form: $(x - 2)(x - 3) = 0$.
3. Apply the Zero Product Property: $x - 2 = 0$ or $x - 3 = 0$.
4. Solve for x: $x = 2$ or $x = 3$.

Choice B is incorrect because these are the constants in the factors, not the solutions. Remember to flip the sign when solving $x - c = 0$. Choice C is incorrect because $1+6=7$, not 5. Choice D is incorrect because $(-1)+(-6)=-7$, not -5.