How do I factorise this expression? [Let’s say it’s x^2 + 5x + 6]

The expression is of the form ax^2 + bx + c. Here, a = 1 and this makes it easier for us. We can also see that b = 5 and c = 6. In general, we have to find two numbers that multiply to get c and add to get b. So here, we must find two numbers which when multiplied give 6 and when added give 5. The only possible pair of numbers is 2 and 3. (Check: 2 + 3 = 5 = b and 2 * 3 = 6 = c). We now set up two pairs of brackets multiplied together, like so: (   )(   ). Now we place x’s at the front of each pair to get (x   )(x  ). Finally, we add the 2 and 3 to the end of each pair, and put in some plus signs, giving us (x+2)(x+3). This is the factorised version of the original expression and is our final answer.