Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:
x – 2, x3 + 3x3 – 12x + 4
Let us divide x3 + 3x2 – 12x + 4 by x – 2
The division process is

Here, the remainder is 0, therefore x – 2 is a factor of x3 + 3x2 – 12x + 4
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