The factors of 3x^2 are 3x and x and the factors of 8 are 8 and 1, or 4 and 2. -8 tells us that there must be a plus sign in one bracket (one factor) and minus in the other. It also tells us that we need to look at the difference between cross products, and not their sum, and the minus sign tells us that the larger of the two cross products must be negative. So we have (3x 1)(x 8) or (3x 8)(x 1) or (3x 2)(x 4) or (3x 4)(x 2) where the sign is yet to be determined. The correspondence no cross product differences are: 23, 5, 10, 2. One of these matches the x coefficient, so since this coefficient is 2 we know that the last in the list of possible factors is the right one, and the larger cross product is 3*2=6 so the minus sign goes in front of 2: (3x+4)(x-2) is the answer.