 Let us look now at the bottoms-up technique, a way to factor trinomials. We discussed in a previous video that when factoring a trinomial where the quadratic coefficient is different from one, many people just become very proficient at trial and error, intelligent guessing and testing, and that is enough for them, but we could also do something that's a bit more systematic. This technique has several steps. The first step is to see whether there is any common factor in the three terms to pull out. That's not the case here. So the second step is to multiply the quadratic coefficient by the constant. 6 times 12 is 72, and now we look at all the factor pairs of 72. 1, 72, 2 times 36, 3 times 24, 4 times 18, 6 times 12, and 8 times 9. And then the third step is to choose a factor pair that adds up to 17. This is the only pair that satisfies that conditions. So now we go to the next step. Take that 8. We are going to create two binomials, x, x, x plus 8, and x plus 9. The next step is to divide the constant terms by the quadratic coefficient, in this case, 6. Now this becomes x plus 4 thirds, and this is x plus 3 halves. If those fractions would have been integers, we would have stopped there. Since they are not, we are going to multiply by an integer so that we get rid of that fraction. Let us multiply the first binomial by 3, 3x plus 4, and let us multiply the second binomial by 2, 2x plus 3. Now, we claim that this is the factorization of this trinomial. In fact, we can check here, 6x squared plus 8x plus 9x plus 12 is indeed what we wanted.