How to factorise the expression x^2 + 8x + 15

We need to get the quadratic expression into the form (x + a)(x + b). If we expand this expression using FOIL, we see that the resulting expression is x² + (a+b)x + ab. We can now find a and b by comparing coefficients. The two numbers, a and b, will add together to make 8, the number in front of x. The two numbers will also multiply together to make 15, the number on its own. By going through the factors of 15, we see that a and b must be 3 and 5.