New formula 3x^2-2x-8 = 3x-8 = -24 right factors of -24 is -6x4 or 6x-4 right so -6+4 = -2 right We exchange -2x to -6x+4x (3x^2-6x)+(4x-8)= 3x(x-2)+4(x-2) rightanswer is (3x+4)(x-2) 

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Please be careful of your use of = signs.  Also it is not clear why you would use the factors of 24 as 6 and 4 without some experimentation.  However, note:  the factors of 3x^2 must be 3x and x.  The factors of 8 must have opposite signs and since the middle sign is negative, the larger middle term product must be negative.  The sum of the middle term binomial products adds to -2x.  8 and 1 will give products too far away from each other so try 4 and 2.  We see (2)(3x) =6x and that leaves a (4)(1x) for the other middle product.  These have a sum of -2x if the sign of 2 is made negative.  Great!  So(3x + 4)(x-2) gives the polynomial desired.You may have a formula that works, but you need to use clear notation, set off with parentheses and other math symbols to show your method.  Of course, completing the square or the quadratic formula always works.