The X-Method

The X-Method:
I hope this helps! I know it may be kind of hard to understand on here, but I hopefully you will get it!

Ex: 6x^2z^2+5xz-4

Step 1: Draw an X and put the middle term (B term) in the top of the X and the first and last terms multiplied in the bottom of the X (AC)






Step 2: Think of two factors that add to get 5, and multiply to get -24.
The two factors are 8 and -3, so you put 8 and -3 on the two sides of the X.

Step 3: Now re-write the new equation.
(xz+8)(xz-3)

Step 4: Use the ‘bottoms up’ method to find the answer. First step to the bottoms up method is to put the A term as the denominator below the 8 and -3.
(xz+8/6)(xz-3/6)
Now you simplify this:
= (xz+4/3)(xz-1/2)
The next step of the bottoms up method is to multiply the denominators by xz, so you basically move the bottom of the fraction up!
= (3xz+4)(2xz-1) This is your answer!

Step 5: Foil to check!
(3xz+4)(2xz-1)= 6x^2z^2-3xz+8xz-4= 6x^2z^2+5xz-4 This is the right answer!