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You would first factor out anything that is common between the 3 parts. 2x2 is the greatest common factor. To pull out the 2x2, you divide each term by 2x2 like so:
12x4/2x2=6x2
10x3/2x2=5x
-12x2/2x2=-6
We now know that 12x4+10x3-12x2= 2x2(6x2+5x-6)
The next step involves using the "slip and slide" method for the trinomial inside the parentheses:
6x2+5x-6
x2+5x-36
(x+9)(x-4)
(x+9/6)(x-4/6)
(x+3/2)(x-2/3)
(2x+3)(3x-2)
Remembering that the result for the slip and slide method only accounts for 6x2+5x-6 we must multiply (2x+3)(3x-2) by 2x2.
Your final answer is 2x2(2x+3)(3x-2).
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