Find the roots of the formula x^2 + 4x + 3 by factorising.

x² + 4x + 3 is a quadratic equation. We're looking for a pair of numbers that add to make 4, and multiply together to make 3. Students should be encouraged to try options (e.g. 2 and 2).
The pair we need is 3 and 1. Because there is no coefficient on the x² term, we don't have to worry about what order they will go in, we'll just have two x + n brackets. So we get: (x + 3)(x + 1).
Then we set (x + 3)(x + 1) = 0 and solve for the two possible values of x (-1 and -3). Students should explain two important learnings points: 1. that setting the formula to zero is asking us the question "what values does this line take when it cuts the x axis?" and 2. that we can use the (x + m)(x + n) = 0 pattern to find x because at any time, at least one of the brackets must equal 0.