Download Box Method! Step-by-Step Directions to factor f(x) = 6x2 – 14x – 12

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)