I'll provide an example to help you. Let's say we were solving and we wanted to factor the quadratic on the left side. We can't do that because the factors of -7 don't add up to 5. So we'd have to use the quadratic formula. The quadratic formula is essentially the last resort that will solve all quadratic equations, so it could be seen as a preferred method. But, unless you can factor the quadratic, it's much easier to solve.
Now let's do another one. for example can be written as and we can easily get and as solutions since plugging them into the factors would produce 0 (from the Zero Product Property). If we used the quadratic formula, it would take more time to plug in the variables and solve when we can just simply factor.
Hopefully, this explanation helps you to think of your discussion post!
