Longer Hunts

When the constant is bigger, there are more factor pairs to check, but the method is the same. To factor $x^{2}+11x+18$, list the pairs of numbers that multiply to 18: 1 and 18, 2 and 9, 3 and 6. Their sums are 19, 11 and 9. You need the pair that adds to 11, so the answer is $\left(x+2\right)\left(x+9\right)$.

Check the pairs in order, starting from 1, so you do not skip one. You can stop as soon as a pair adds to the right number. Only one pair of positive numbers can work, because as the first factor gets bigger, the sum keeps changing in the same direction.

If you have checked every factor pair and none adds to the middle coefficient, the trinomial cannot be factored with whole numbers.