What do you mean by "trial solutions"? Were you just substituting numbers for x and seeing if they worked out? If that is what you mean I can't see why it would be a better procedure than using the quadratic formula.
Yes, I meant substituting numbers for x and seeing if they worked out. To get integer solutions, it's enough to try divisors of the constant term. Try it yourself. It's faster.
Yes, it is faster for small integer values. Most numbers aren't small integer values. Test questions are usually designed to give nice clean answers but the real world isn't like that. They were trying to test your ability to solve quadratic equations in the general case. Your approach doesn't demonstrate that ability.
