Question

How do you factor `n^2-5n+6`?

Answer 1

Notice that `5 = 2+3` and `6 = 2*3`, so

`(n - 2)(n - 3) = (n*n)-(2*n)-(3*n)+(2*3)`

`= n^2-(2+3)n+(2*3)`

`= n^2-5n+6`

In general `(x + a)(x + b) = x^2 + (a+b)x + ab` so if you can spot two numbers `a` and `b` such that their sum is the coefficient of `x` and their product is the constant term then you can quickly factorise such a quadratic formula.