THIS IS ALSO CALLED THE REVERSE FOIL METHOD

Step 1: The sign of the last term (6) is positive. Therefore the signs of the two binomial factors are the same (since multiplying like signs gives a positive number; if the sign had been negative, we know the binomial factors would have different signs).

Step 2: The variable parts of the binomial factors are both going to be x, because only x * x (the multiplication of the "firsts") will give me x^{2}.

Step 3: You know the number parts of the binomials have to be multiply to be 6, since you will be multiplying them together to get the last term of the polynomial. Factors of 6 are 1 and 6, and 2 and 3.

Step 4: You know the number parts of the binomials have to add up to 5, because in FOIL, the "OI" parts add up to the x-coefficient. Which of the factors of 6, that you noted in the step above, add up to 5? The answer to that is 2 and 3.

Step 5: So the variable parts of the binomial factors are both x, and the number parts of the binomial factors are 2 and 3. Therefore my factors are (x + 2)(x + 3).

Step 6: check your work by multiplying the factors I come up with to make sure you come up with the polynomial you started with. (x + 2)(x +3) = x^{2} + 5x + 6, so your factors are correct.