1. The problem statement, all variables and given/known data Factor this quadratic expression completely. 126x² - 15x - 66 2. Relevant equations 3. The attempt at a solution 126x² - 15x - 66 (9x+6)(14x-11) I'm a good ways past this subject, but I find that it always takes me longer than some to complete these problems. If the coefficients are low numbers, I can "guess and check" and get the right combination. When the coefficients get into the higher numbers I run into trouble. I always resort to the "box" method when the factors are not really apparent, but my professor says that I should be using "guess and check" as it's much more efficient. Here is how I would solve the problem.. 126x² - 15x - 66 3(42x² -5x - 22) //factor out the GCF Now I take 42*-22, and think of factors of that which would make the -5. -924=(-21*44)=(-22*42)=(-33*28) Ok, so 33-28=-5 Now I use the "box method" 42x² | 33x -28x | -66 Factoring out the "box" 14x 11 42x² | 33x 3x -28x | -66 -2 So now I know the sets of numbers that I can use, I just adjust the signs to work.. 3(14x-11)(3x+2) or (9x+6)(14x-11) I know that I don't have to factor out the GCF, I just did it that way to show my steps. I am told by everyone that the "guess and check" method is much faster, easier, and generally better to use. Am I guessing-and-checking wrong or something? At least this box method is systematic, I know I will arrive at the right answer, and not based on chance. Any other tips on how to do this would be greatly appreciated.