If you mean: (x-4)(x+12) then it is x^2 +8x -48
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x4 + 7x2 - 60 = x4 + 12x2 - 5x2 - 60 = x2(x2 + 12) - 5(x2 +12) = (x2 - 5)(x2 +12)
x4+6x3-2x-12 (x3-2)(x+6)
I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28
sqrt(x4) = x4/2 = x2
N = x4 x8 = x4+4 = (x4)2 = N2