Theory
A quadratic has an x² term. In this lesson, the coefficient of x² is 1, so the brackets usually start as (x ...)(x ...).
For x² + bx + c, look for two numbers that multiply to c and add to b.
Those two numbers go into the brackets: (x + p)(x + q).
If c is positive, the signs in the brackets are usually the same. If c is negative, one bracket is usually plus and the other is minus.
If the question says factorise, stop when the expression is in brackets. If the question says solve, continue by setting each bracket equal to zero.
For Edexcel method marks, show the pair of numbers or a clear factorising step before writing the final brackets.
Key rule(x + p)(x + q) = x² + (p + q)x + pq