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Box Method! Step-by-Step Directions to factor f(x) = 6x2 – 14x – 12 Step 0) Pull out any common factors: 2(3x2 – 7x – 6) Step 1) Place the x2 term and the number term in the box like so: 3x2 -6 Step 2) Ignoring any negative signs (and the x2), multiply the numbers in the box 3 * 6 = 18 Step 3) List all the pairs of numbers you can multiply together to get your number from step 2 18: 6 & 3; 2 & 9; 1 & 18 Step 4) *If the c term (the lone number) in your original expression is negative, you will look for a pair in step 3 that has a difference of the b term (the number with the x). *If the c term is positive, you will look for a pair in step 3 that has a sum of the b term. I need two numbers that have a difference of 7 since my c term is negative (-6): 2 & 9 Step 5) Put those numbers into the empty boxes (doesn’t matter which) and put x’s with them 3x2 2x 9x -6 Step 6) Decide which of those numbers (if any) need to be negative to add to the b term (middle number with the x) To get a -7x, I need the 9x to be negative, so that 2x + -9x = -7x 3x2 2x -9x -6 Step 7) Pull out the greatest common factors for the first row and first column: 3x x 3x2 2x -9x -6 Step 8) Finish the sides of the table: “what do I need to multiply this by to get this?” 3x 2 2 x 3x 2x -3 -9x -6 Step 9) You now have your factors on the top and side: (x – 3)(3x + 2) and don’t forget anything you pulled out at the beginning: 2(x – 3)(3x + 2)