1)  3x^3 - 12x^2 - 2x + 8 = 


        Apply grouping.   Look: there are coefficients (3,-12) at x^3 and x^2    -  and  (-2,8)  at x  and the constant term.
        It gives you an idea how to group:


    3x^3 - 12x^2 - 2x + 8 = (3x^3 - 12x^2) - (2x -8) = 3x^2*(x-4) - 2*(x-4)


        Now use that (x-4) is the common factor


    = (x-4)*(3x^2 - 2).


    Thus this factoring is COMPLETED over the polynomials with integer coefficients.

2)  4x^4  - 16x^2 - 9x^2 + 36


        THE SAME IDEA WORKS again:


    4x^4  - 16x^2 - 9x^2 + 36 = (4x^4  - 16x^2) - (9x^2 - 36) = 4x^2*(x^2-4) - 9*(x^2-4) = (x^2-4)*(4x^2-9) = (x-2)*(x+2)*(2x-3)*(2x+3).