First notice that the function is a quadratic and so will have two factors. Since the coefficient of x^2 is 1, the factors will be of the form: (x+a) (x+b)
We will assume that a and b are integers.
Hence, we need to find a and b such that the product of the factors is equal to the given quadratic function. Now consder the absoute value of constant term, 3. Since 3 is prime its only factors are 3 and 1. Since the constant term is positive, a and b can only be 3 and 1 or -3 and -1. Finally observe that the coefficient of x is positive 4 and that the sum of 3 and 1 is positive 4. Thus, a and b must be 3 and 1 (or the other way around, but this makes no difference to our factorisation) Hence we see that: x^2+4x+3 = (x+3) (x+1)
